Sparser Johnson-Lindenstrauss Transforms

We give two different and simple constructions for dimensionality reduction in $\ell_2$ via linear mappings that are sparse: only an $O(\varepsilon)$-fraction of entries in each column of our embedding matrices are non-zero to achieve distortion $1+\varepsilon$ with high probability, while still achieving the asymptotically optimal number of rows. These are the first constructions to provide subconstant sparsity for all values of parameters, improving upon previous works of Achlioptas (JCSS 2003) and Dasgupta, Kumar, and Sarl\'{o}s (STOC 2010). Such distributions can be used to speed up applications where $\ell_2$ dimensionality reduction is used.Comment: v6: journal version, minor changes, added Remark 23; v5: modified abstract, fixed typos, added open problem section; v4: simplified section 4 by giving 1 analysis that covers both constructions; v3: proof of Theorem 25 in v2 was written incorrectly, now fixed; v2: Added another construction achieving same upper bound, and added proof of near-tight lower bound for DKS schem

Do roads cause deforestation? Using satellite images in econometric analysis of land use

In this paper we demonstrate how satellite images and other geographic data can be used to predict land use. A cross-section model of land use is estimated with data for a region in central Mexico. Parameters from the model are used to examine the effects of reduced human activity. If variables that proxy human influence are changed to reflect reduced impact, "forest" area increases and "irrigated crop" area is reduced.geographic data, land use, remotely sensed data, spatial econometrics.

Geology and Geochemistry of the Ship Creek and Monashka Creek reservoirs, Southcentral Alaska

Graywacke from the Ship Creek watershed, dissolves incongruently in distilled water. The dissolution appears to follow a first-order rate law which in integrated form is: k = -2.303/t log No-Q/No where No is the concentration in ppm of Ca, Mg, Na or K in the graywacke, Q is the total quantity of these ions leached in time t(days), k is the rate constant in days-1. Experimentally derived rate constants for the dissolution of graywacke in distilled water at 5oC are log k+2CA, -4.128 day-1; log k+2Mg, -6.174 day-1; log k+Na, -5.800 day-1; and log k+K, -5.249 day-1. The above constants are for 40 to +100 mesh graywacke. A surface area correction term must be inserted in the above equation if it is applied to a different size fraction. Using the above equation and rate constants, the chemical composition of a water in contact with graywacke was calculated. With the exception of magnesium, the agreement between the calculated composition and that of Ship Creek water was good. Assuming that the groundwater in the Ship Creek watershed contacts about 1.5X104cm2 graywacke per liter, 120 to 360 days are required at 5oC to produce the concentration of ions observed in Ship Creek. Release of exchangeable H+ from the soil mat to the reservoir water will not significant1y lower the pH of the water. Leaching of heavy metals from sulfides contained in the bedrock of the two watersheds does not pose a water quality hazard. Lineaments in the bedrock at Monashka Creek may provide channels through which water may seep from the reservoir. These are not expected to pose a problem in retaining water in the reservoir, but they may result in small, new springs down grade from the reservoir.The work upon which this report is based was supported by funds provided by the United States Department of the Interior, Office of Water Resources Research and Technology, as authorized by the Water Resources Research Act of 1964, Public Law 88-379, as amended. (Project A-045-ALAS

Bounded Independence Fools Degree-2 Threshold Functions

Let x be a random vector coming from any k-wise independent distribution over {-1,1}^n. For an n-variate degree-2 polynomial p, we prove that E[sgn(p(x))] is determined up to an additive epsilon for k = poly(1/epsilon). This answers an open question of Diakonikolas et al. (FOCS 2009). Using standard constructions of k-wise independent distributions, we obtain a broad class of explicit generators that epsilon-fool the class of degree-2 threshold functions with seed length log(n)*poly(1/epsilon). Our approach is quite robust: it easily extends to yield that the intersection of any constant number of degree-2 threshold functions is epsilon-fooled by poly(1/epsilon)-wise independence. Our results also hold if the entries of x are k-wise independent standard normals, implying for example that bounded independence derandomizes the Goemans-Williamson hyperplane rounding scheme. To achieve our results, we introduce a technique we dub multivariate FT-mollification, a generalization of the univariate form introduced by Kane et al. (SODA 2010) in the context of streaming algorithms. Along the way we prove a generalized hypercontractive inequality for quadratic forms which takes the operator norm of the associated matrix into account. These techniques may be of independent interest.Comment: Using v1 numbering: removed Lemma G.5 from the Appendix (it was wrong). Net effect is that Theorem G.6 reduces the m^6 dependence of Theorem 8.1 to m^4, not m^

GSFC Ada programming guidelines

A significant Ada effort has been under way at Goddard for the last two years. To ease the center's transition toward Ada (notably for future space station projects), a cooperative effort of half a dozen companies and NASA personnel was started in 1985 to produce programming standards and guidelines for the Ada language. The great richness of the Ada language and the need of programmers for good style examples makes Ada programming guidelines an important tool to smooth the Ada transition. Because of the natural divergence of technical opinions, the great diversity of our government and private organizations and the novelty of the Ada technology, the creation of an Ada programming guidelines document is a difficult and time consuming task. It is also a vital one. Steps must now be taken to ensure that the guide is refined in an organized but timely manner to reflect the growing level of expertise of the Ada community

Dynamic Web File Format Transformations with Grace

Web accessible content stored in obscure, unpopular or obsolete formats represents a significant problem for digital preservation. The file formats that encode web content represent the implicit and explicit choices of web site maintainers at a particular point in time. Older file formats that have fallen out of favor are obviously a problem, but so are new file formats that have not yet been fully supported by browsers. Often browsers use plug-in software for displaying old and new formats, but plug-ins can be difficult to find, install and replicate across all environments that one may use. We introduce Grace, an http proxy server that transparently converts browser-incompatible and obsolete web content into web content that a browser is able to display without the use of plug-ins. Grace is configurable on a per user basis and can be expanded to provide an array of conversion services. We illustrate how the Grace prototype transforms several image formats (XBM, PNG with various alpha channels, and JPEG 2000) so they are viewable in Internet Explorer.Comment: 12 pages, 9 figure