Fast Algorithms and Efficient Statistics: N-point Correlation Functions

We present here a new algorithm for the fast computation of N-point correlation functions in large astronomical data sets. The algorithm is based on kdtrees which are decorated with cached sufficient statistics thus allowing for orders of magnitude speed-ups over the naive non-tree-based implementation of correlation functions. We further discuss the use of controlled approximations within the computation which allows for further acceleration. In summary, our algorithm now makes it possible to compute exact, all-pairs, measurements of the 2, 3 and 4-point correlation functions for cosmological data sets like the Sloan Digital Sky Survey (SDSS; York et al. 2000) and the next generation of Cosmic Microwave Background experiments (see Szapudi et al. 2000).Comment: To appear in Proceedings of MPA/MPE/ESO Conference "Mining the Sky", July 31 - August 4, 2000, Garching, German

Wired warfare 3.0: protecting the civilian population during cyber operations

As a general matter, international humanitarian law is up to the task of providing the legal framework for cyber operations during an armed conflict. However, two debates persist in this regard, the resolution of which will determine the precise degree of protection the civilian population will enjoy during cyber operations. The first revolves around the meaning of the term “attack” in various conduct of hostilities rules, while the second addresses the issue of whether data may be considered an object such that operations destroying or altering it are subject to the prohibition on attacking civilian objects and that such effects need be considered when considering proportionality and the taking of precautions in attack. Even if these debates were to be resolved, the civilian population would still face risks from the unique capabilities of cyber operations. This article proposes two policies which parties to a conflict should consider adopting in order to ameliorate such risks. They are both based on the premise that military operations must reflect a balance between military concerns and the interest of States in prevailing in the conflict

Fixed Parameter Undecidability for Wang Tilesets

Deciding if a given set of Wang tiles admits a tiling of the plane is decidable if the number of Wang tiles (or the number of colors) is bounded, for a trivial reason, as there are only finitely many such tilesets. We prove however that the tiling problem remains undecidable if the difference between the number of tiles and the number of colors is bounded by 43. One of the main new tool is the concept of Wang bars, which are equivalently inflated Wang tiles or thin polyominoes.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

The strong Lefschetz property in codimension two

Every artinian quotient of $K[x,y]$ has the strong Lefschetz property if $K$ is a field of characteristic zero or is an infinite field whose characteristic is greater than the regularity of the quotient. We improve this bound in the case of monomial ideals. Using this we classify when both bounds are sharp. Moreover, we prove that the artinian quotient of a monomial ideal in $K[x,y]$ always has the strong Lefschetz property, regardless of the characteristic of the field, exactly when the ideal is lexsegment. As a consequence we describe a family of non-monomial complete intersections that always have the strong Lefschetz property.Comment: 18 pages, 1 figure; v2: Updated history and reference

Hopf Bifurcation and Chaos in a Single Inertial Neuron Model with Time Delay

A delayed differential equation modelling a single neuron with inertial term is considered in this paper. Hopf bifurcation is studied by using the normal form theory of retarded functional differential equations. When adopting a nonmonotonic activation function, chaotic behavior is observed. Phase plots, waveform plots, and power spectra are presented to confirm the chaoticity.Comment: 12 pages, 7 figure

What similar physical processes occur on both Earth and Mars?

This NASA Module investigation compares and contrasts physical processes that occur on Both Earth and Mars. Students are given unidentified images of Earth and Mars. Their task is to arrange the images into pairs that show evidence of similar physical processes. Then they identify each image as one of Earth or of Mars by comparing and contrasting physical features that they observe in the image pairs. It includes teacher background materials and an answer key where appropriate. Educational levels: High school, Middle school