On the Chromatic Roots of Generalized Theta Graphs
The generalized theta graph ?s1, ?, sk consists of a pair of endvertices joined by k internally disjoint paths of lengths s1, ?, sk?1. We prove that the roots of the chromatic polynomial ? of a k-ary generalized theta graph all lie in the disc|z?1|?1+o(1)]k/logk, uniformly in the path lengths si. Moreover, we prove that ?2, ?, 2?K2, k indeed has a chromatic root of modulus 1+o(1)]k/logk. Finally, for k?8 we prove that the generalized theta graph with a chromatic root that maximizes |z?1| is the one with all path lengths equal to 2; we conjecture that this holds for all k.

title: The Complexity of Generalized Graph Colorings
abstract: Given a graph property P and positive integer k, a P k-coloring of a graph G is an assignment of one of k colors to each vertex of the graph so that the subgraphs induced by each color class have property P. This notion generalizes the standard definition of graph coloring, and has been investigated for many properties. We consider here the complexity of the decision problem. In particular, for the property —G, of not containing an induced subgraph isomorphic to G, we conjecture (and provide strong evidence) that —G k-colorability is NP-complete whenever G has order at least 3 and k ⩾ 2. The techniques rely on new NP-completeness results for hypergraph colorings.

title: On chromatic roots with negative real part

title: Average independence polynomials
abstract: The independence polynomial of a graph G is the function i(G, x) = Σ k ≥ 0 ik xk, where ik is the number of independent sets of vertices in G of cardinality k. We investigate here the average independence polynomial, where the average is taken over all independence polynomials of (labeled) graphs of order n. We prove that while almost every independence polynomial has a nonreal root, the average independence polynomials always have all real, simple roots.

title: The existence of uniquely -G colourable graphs
abstract: Given graphs F and G and a nonnegative integer k , a function π : V ( F ) → 1, …, k is a − G k-colouring of F if no induced copy of is monochromatic; F is − G k-chromatic if F has a − G k -colouring but no − G ( k − 1)-colouring. Further, we say F is uniquely − G k -colourable if F is − G k -chromatic and, up to a permutation of colours, it has only one − G k -colouring. Such notions are extensions of the well-known corresponding definitions from chromatic theory. It was conjectured that for all graphs G of order at least two and all positive integers k there exist uniquely − G k -colourable graphs. We prove the conjecture and show that, in fact, in all cases infinitely many such graphs exist.

title: A ramsey type problem concerning vertex colourings
abstract: Let H → k v G denote the fact that for every function π: V ( H ) → {1, …, k } there is an induced subgraph G ′ of H with G ′ ≅ G and V ( G ′) ⊆ π −1 ( i ) for some i . Folkman has shown that for all graphs G and for all positive integers k such a graph H exists. We examine here f ( G , k ), the minimum order of a graph H for which H → k v G . We show that for any fixed integer k ≥ 2 there are positive constants C 1 and C 2 such that C 1 n 2 ≤ max{ f ( G , k ): | V ( G )| = n } ≤ C 2 n 2 log 2 n .

title: Applications of Artificial Intelligence
abstract: One of the aims of artificial intelligence has been to make machines behave intelligently as humans do. Thus the study of artificial intelligence includes the study of how humans acquire and apply knowledge, reason under uncertainty and in complex environments, and how they do planning and solve problems. Knowledge-based automation deals with the application of artificial intelligence to a production environment in order to reduce the involvement of human beings to a minimum.

title: A Qualitative Physics Based on Confluences
abstract: A qualitative physics predicts and explains the behavior of mechanisms in qualitative terms. The goals for the qualitative physics are (1) to be far simpler than the classical physics and yet retain all the important distinctions (e.g., state, oscillation, gain, momentum) without invoking the mathematics of continuously varying quantities and differential equations, (2) to produce causal accounts of physical mechanisms that are easy to understand, and (3) to provide the foundations for commonsense models for the next generation of expert systems. This paper presents a fairly encompassing account of qualitative physics. First, we discuss the general subject of naive physics and some of its methodological considerations. Second, we present a framework for modeling the generic behavior of individual components of a device based on the notions of qualitative differential equations (confluences) and qualitative state. This requires developing a qualitative version of the calculus. The modeling primitives induce two kinds of behavior, intrastate and interstate, which are governed by different laws. Third, we present algorithms for determining the behavior of a composite device from the generic behavior of its components. Fourth, we examine a theory of explanation for these predictions based on logical proof. Fifth, we introduce causality as an ontological commitment for explaining how devices behave.

title: The Ribonuclease P Database
abstract: Ribonuclease P is responsible for the removal of leader sequences from tRNA precursors. Ribonuclease P is a ribonucleoprotein, and in bacteria the RNA subunit alone is catalytically active in vitro, i.e. it is a ribozyme. The Ribonuclease P Database is a compilation of ribonuclease P sequences, sequence alignments, secondary structures, three-dimensional models, and accessory information, available via the World Wide Web.

title: The ribonuclease P database
abstract: Ribonuclease P is responsible for the 5'-maturation of tRNA precursors. Ribonuclease P is a ribonucleoprotein, and in bacteria (and some Archaea) the RNA subunit alone is catalytically active in vitro, i.e. it is a ribozyme. The Ribonuclease P Database is a compilation of ribonuclease P sequences, sequence alignments, secondary structures, three-dimensional models and accessory information, available via the World Wide Web at the following URL: http://www.mbio.ncsu.edu/RNaseP/home .html

title: A Macintosh Hypercard compilation of small subunit ribosomal RNA sequences
abstract: Molecular biologists, particularly those working with unicellular organisms, are becoming increasingly aware of the importance of understanding the phylogenetic (evolutionary) relationships between their model systems and other organisms. Currently, the best method for determining quantitatively the phylogenetic relationships in a group of organisms is the analysis of small subunit ribosomal RNA (ssu RNA) sequences (Woese, 1984). To assist in this type of analysis, the Ribosomal RNA Database Project (RDP) collects and distributes ssu rRNA sequences and software for phylogenetic analysis (Olsen et al., 1991). The ssu rRNA sequence stack is collection of almost 500 aligned ssu rRNA sequences taken from the first public release of the RDP sequence collection. The ssu rRNA sequence stack consists of a series of 'cards' each containing the ssu rRNA sequence of a single organism , from which the sequence can be copied (either with or without alignment information) or saved as a text file in GenBank format. Navigation in the stack is via a series of linked phylogenetic trees. Starting with a 'universal tree', clicking on the branch of interest takes the user to increasingly more specific and detailed trees. In the most specific trees, clicking on a branch either takes the user directly to the sequence card (if only one sequence is available representing that group) or presents the user with a pop-up menu of available sequences. Alternatively, the user can choose the desired sequence from a list containing the names of all of the available sequences, or choose to search the sequence names for a specific character string. The ssu rRNA sequence stack is written in Hypertalk v. 2.1, and requires v. 2.0 (or greater) of HyperCard, which in turn requires at least a Macintosh Plus, 1 Mbyte of RAM, the Macintosh operating system v 6.0.5 (or greater), and preferably a hard disk drive. The ssu rRNA sequence stack is available by anonymous FTP from ftp.bio.indiana.edu, by E-mail from the author at jwbrown@bio.indiana.edu or brownjw@iubacs.bitnet, or on floppy disk (enclose a single formatted high-density disk) free of charge on written request to the author.