Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment

Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of affine point matching, obtaining an expression for the range of affine-invariant values consistent with bounded uncertainty. This analysis reveals that the range of affine-invariant values depends on the actual $x$-$y$-positions of the features, i.e. with uncertainty, affine representations are not invariant with respect to the Cartesian coordinate system. We analyze the effect of this on geometric hashing and alignment recognition methods.

A Note of Zipf's Law, Natural Languages, and Noncoding DNA Regions

In Phys. Rev. Letters (73:2), Mantegna et al. conclude on the basis of Zipf rank frequency data that noncoding DNA sequence regions are more like natural languages than coding regions. We argue on the contrary that an empirical fit to Zipf"s "law" cannot be used as a criterion for similarity to natural languages. Although DNA is a presumably "organized system of signs" in Mandelbrot"s (1961) sense, and observation of statistical featurs of the sort presented in the Mantegna et al. paper does not shed light on the similarity between DNA's "gramar" and natural language grammars, just as the observation of exact Zipf-like behavior cannot distinguish between the underlying processes of tossing an M-sided die or a finite-state branching process.

Supporting Dynamic Languages on the Java Virtual Machine

In this note, I propose two extensions to the Java virtual machine (or VM) to allow dynamic languages such as Dylan, Scheme and Smalltalk to be efficiently implemented on the VM. These extensions do not affect the performance of pure Java programs on the machine. The first extension allows for efficient encoding of dynamic data; the second allows for efficient encoding of language-specific computational elements.