Embedded graph invariants in Chern-Simons theory

Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines - an embedded graph invariant. Using a slight generalization of the variational method, lowest-order results for invariants for arbitrary valence graphs are derived; gauge invariant operators are introduced; and some higher order results are found. The method used here provides a Vassiliev-type definition of graph invariants which depend on both the embedding of the graph and the group structure of the gauge theory. It is found that one need not frame individual vertices. Though, without a global projection of the graph, there is an ambiguity in the relation of the decomposition of distinct vertices. It is suggested that framing may be seen as arising from this ambiguity - as a way of relating frames at distinct vertices.Comment: 20 pages; RevTex; with approx 50 ps figures; References added, introduction rewritten, version to be published in Nuc. Phys.

On Yao's method of translation

Machine Translation, i.e., translating one kind of natural language to another kind of natural language by using a computer system, is a very important research branch in Artificial Intelligence. Yao developed a method of translation that he called ``Lexical-Semantic Driven". In his system he introduced 49 ``relation types" including case relations, event relations, semantic relations, and complex relations. The knowledge graph method is a new kind of method to represent an interlingua between natural languages. In this paper, we will give a comparison of these two methods. We will translate one Chinese sentence cited in Yao�s book by using these two methods. Finally, we will use the relations in knowledge graph theory to represent the ``relations" in Lexical-Semantic Driven, and partition the relations in Lexical-Semantic Driven into groups according to the relations in knowledge graph theory

Counterbalancing for serial order carryover effects in experimental condition orders

Reactions of neural, psychological, and social systems are rarely, if ever, independent of previous inputs and states. The potential for serial order carryover effects from one condition to the next in a sequence of experimental trials makes counterbalancing of condition order an essential part of experimental design. Here, a method is proposed for generating counterbalanced sequences for repeated-measures designs including those with multiple observations of each condition on one participant and self-adjacencies of conditions. Condition ordering is reframed as a graph theory problem. Experimental conditions are represented as vertices in a graph and directed edges between them represent temporal relationships between conditions. A counterbalanced trial order results from traversing an Euler circuit through such a graph in which each edge is traversed exactly once. This method can be generalized to counterbalance for higher order serial order carryover effects as well as to create intentional serial order biases. Modern graph theory provides tools for finding other types of paths through such graph representations, providing a tool for generating experimental condition sequences with useful properties