Digital cartography of Mars

A medium-resolution Digital Image Model (DIM) of Mars is being compiled. A DIM is a mosaic of radiometrically corrected, photometrically modelled spacecraft images displaying accurate reflectance properties at uniform resolution, and geometrically tied to the best available control. The Mars medium-resolution DIM contains approximately 4700 Viking Orbiter image frames that were used to compile the recently completed 1:2,000,000-scale controlled photomosaic series of Mars. This DIM provides a planimetric control base to which all other Mars maps will be registered. A similar control base of topographic elevations (Digital Terrain Model, or DTM) is also being compiled. These products are scheduled for completion in 1989

Risk analysis methodology survey

NASA regulations require that formal risk analysis be performed on a program at each of several milestones as it moves toward full-scale development. Program risk analysis is discussed as a systems analysis approach, an iterative process (identification, assessment, management), and a collection of techniques. These techniques, which range from simple to complex network-based simulation were surveyed. A Program Risk Analysis Handbook was prepared in order to provide both analyst and manager with a guide for selection of the most appropriate technique

Performance of binary FSK data transmission systems

Matched-filter detection of binary signals is discussed in terms of the probability of bit error. The equations for the probability of error are derived for coherent phase shift keying, and coherent frequency shift keying (FSK). Suboptimum detection of FSK signals is also discussed for discriminators

Operations planning and analysis handbook for NASA/MSFC phase B development projects

Current operations planning and analysis practices on NASA/MSFC Phase B projects were investigated with the objectives of (1) formalizing these practices into a handbook and (2) suggesting improvements. The study focused on how Science and Engineering (S&E) Operational Personnel support Program Development (PD) Task Teams. The intimate relationship between systems engineering and operations analysis was examined. Methods identified for use by operations analysts during Phase B include functional analysis, interface analysis methods to calculate/allocate such criteria as reliability, Maintainability, and operations and support cost

Status and future of extraterrestrial mapping programs

Extensive mapping programs have been completed for the Earth's Moon and for the planet Mercury. Mars, Venus, and the Galilean satellites of Jupiter (Io, Europa, Ganymede, and Callisto), are currently being mapped. The two Voyager spacecraft are expected to return data from which maps can be made of as many as six of the satellites of Saturn and two or more of the satellites of Uranus. The standard reconnaissance mapping scales used for the planets are 1:25,000,000 and 1:5,000,000; where resolution of data warrants, maps are compiled at the larger scales of 1:2,000,000, 1:1,000,000 and 1:250,000. Planimetric maps of a particular planet are compiled first. The first spacecraft to visit a planet is not designed to return data from which elevations can be determined. As exploration becomes more intensive, more sophisticated missions return photogrammetric and other data to permit compilation of contour maps

Restricted Invertibility and the Banach-Mazur distance to the cube

We prove a normalized version of the restricted invertibility principle obtained by Spielman-Srivastava. Applying this result, we get a new proof of the proportional Dvoretzky-Rogers factorization theorem recovering the best current estimate. As a consequence, we also recover the best known estimate for the Banach-Mazur distance to the cube: the distance of every n-dimensional normed space from \ell_{\infty}^n is at most (2n)^(5/6). Finally, using tools from the work of Batson-Spielman-Srivastava, we give a new proof for a theorem of Kashin-Tzafriri on the norm of restricted matrices.Comment: to appear in Mathematik

Cartography of irregularly shaped satellites

Irregularly shaped satellites, such as Phobos and Amalthea, do not lend themselves to mapping by conventional methods because mathematical projections of their surfaces fail to convey an accurate visual impression of the landforms, and because large and irregular scale changes make their features difficult to measure on maps. A digital mapping technique has therefore been developed by which maps are compiled from digital topographic and spacecraft image files. The digital file is geometrically transformed as desired for human viewing, either on video screens or on hard copy. Digital files of this kind consist of digital images superimposed on another digital file representing the three-dimensional form of a body

Twice-Ramanujan Sparsifiers

We prove that every graph has a spectral sparsifier with a number of edges linear in its number of vertices. As linear-sized spectral sparsifiers of complete graphs are expanders, our sparsifiers of arbitrary graphs can be viewed as generalizations of expander graphs. In particular, we prove that for every $d>1$ and every undirected, weighted graph $G=(V,E,w)$ on $n$ vertices, there exists a weighted graph $H=(V,F,\tilde{w})$ with at most \ceil{d(n-1)} edges such that for every $x \in \R^{V}$, $$x^{T}L_{G}x \leq x^{T}L_{H}x \leq (\frac{d+1+2\sqrt{d}}{d+1-2\sqrt{d}})\cdot x^{T}L_{G}x$$ where $L_{G}$ and $L_{H}$ are the Laplacian matrices of $G$ and $H$, respectively. Thus, $H$ approximates $G$ spectrally at least as well as a Ramanujan expander with $dn/2$ edges approximates the complete graph. We give an elementary deterministic polynomial time algorithm for constructing $H$