In this technical report we present a self-contained introduction to algorithms that solve sparse linear systems by message passing on a junction tree (a.k.a. clique tree). When solving the systemAx = b whereA is a sparse n×nmatrix, these methods require O(n · w3) time and O(n · w2) space, where w is the treewidth of A’s sparsity graph. These algorithms are useful for parallel or distributed so...

Geometric algebra is a consistent computational framework in which to define geometric primitives and their relationships. This algebraic approach contains all geometric operators and permits specification of constructions in a coordinate-free manner. Thus, the ideas of geometric algebra are important for developers of CAD systems. This paper gives an introduction to the elements of geometric a...

In this chapter we provide a brief introduction to multidimensional codes. In particular, we focus on product codes and other similar codes that use parity checks over multidimensional arrays. We present a brief introduction to product codes and their properties. We then focus on multidimensional codes based on single parity-check constituent codes. We provide two applications that illustrate t...

I Introduction What is the epistemic significance of discovering that one of your beliefs depends on an irrelevant causal factor? Suppose that you have a relatively high degree of belief in some proposition. Suppose that you then come to learn that your belief was (in part) caused by an irrelevant factor, a factor that does not bear on the truth of the proposition or on your possession of evide...

This material is covered in Cormen, Leiserson, Rivest and Smith “Introduction to Algorithms” — Appendix C. You can also look at the lecture notes for MIT course 6.042 Mathematics for Computer Science by Lehman and Leighton on http://theory.lcs.mit.edu/∼e lehman/mathcs.pdf — Chapters 18 to 24. (See also http://theory.lcs.mit.edu/classes/6.042/spring05/) You should also take a look at Trevisan’s ...

This investigation focused on providing a more nuanced understanding of the message retention-attitude (cognition-affect) relationship in new product introductions. Using advertising and publicity as independent and combined promotional tools, this investigation focused on determining an effective approach to boost the strength of the retention-attitude relationship as well as the level of new ...

1 Thin film specifications continue to push the envelope of manufacturing capabilities. Many advanced commercial and military applications require ultra low loss films that are extremely difficult to deposit using conventional Electron beam or Ion Assisted Deposition (IAD) technology. Ring Laser Gyroscope (RLG) mirrors for instance require high packing density, minimal defects, and negligible a...