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.

Toward a Theory of Representation Design

This research is concerned with designing representations for analytical reasoning problems (of the sort found on the GRE and LSAT). These problems test the ability to draw logical conclusions. A computer program was developed that takes as input a straightforward predicate calculus translation of a problem, requests additional information if necessary, decides what to represent and how, designs representations capturing the constraints of the problem, and creates and executes a LISP program that uses those representations to produce a solution. Even though these problems are typically difficult for theorem provers to solve, the LISP program that uses the designed representations is very efficient.

A Model for Deliberation, Action, and Introspection

This thesis investigates the problem of controlling or directing the reasoning and actions of a computer program. The basic approach explored is to view reasoning as a species of action, so that a program might apply its reasoning powers to the task of deciding what inferences to make as well as deciding what other actions to take. A design for the architecture of reasoning programs is proposed. This architecture involves self-consciousness, intentional actions, deliberate adaptations, and a form of decision-making based on dialectical argumentation. A program based on this architecture inspects itself, describes aspects of itself, and uses this self-reference and these self-descriptions in making decisions and taking actions. The program's mental life includes awareness of its own concepts, beliefs, desires, intentions, inferences, actions, and skills. All of these are represented by self-descriptions in a single sort of language, so that the program has access to all of these aspects of itself, and can reason about them in the same terms.

Belief Propagation and Revision in Networks with Loops

Local belief propagation rules of the sort proposed by Pearl(1988) are guaranteed to converge to the optimal beliefs for singly connected networks. Recently, a number of researchers have empirically demonstrated good performance of these same algorithms on networks with loops, but a theoretical understanding of this performance has yet to be achieved. Here we lay the foundation for an understanding of belief propagation in networks with loops. For networks with a single loop, we derive ananalytical relationship between the steady state beliefs in the loopy network and the true posterior probability. Using this relationship we show a category of networks for which the MAP estimate obtained by belief update and by belief revision can be proven to be optimal (although the beliefs will be incorrect). We show how nodes can use local information in the messages they receive in order to correct the steady state beliefs. Furthermore we prove that for all networks with a single loop, the MAP estimate obtained by belief revisionat convergence is guaranteed to give the globally optimal sequence of states. The result is independent of the length of the cycle and the size of the statespace. For networks with multiple loops, we introduce the concept of a "balanced network" and show simulati.

Fast Sorting on a Distributed-Memory Architecture

We consider the often-studied problem of sorting, for a parallel computer. Given an input array distributed evenly over p processors, the task is to compute the sorted output array, also distributed over the p processors. Many existing algorithms take the approach of approximately load-balancing the output, leaving each processor with Θ(n/p) elements. However, in many cases, approximate load-balancing leads to inefficiencies in both the sorting itself and in further uses of the data after sorting. We provide a deterministic parallel sorting algorithm that uses parallel selection to produce any output distribution exactly, particularly one that is perfectly load-balanced. Furthermore, when using a comparison sort, this algorithm is 1-optimal in both computation and communication. We provide an empirical study that illustrates the efficiency of exact data splitting, and shows an improvement over two sample sort algorithms.