On chromatic roots with negative real part

title: Graph coloring satisfying restraints
abstract: For an integer k ⩾2, a proper k-restraint on a graph G is a function from the vertex set of G to the set of k -colors. A graph G is amenably k-colorable if, for each nonconstant proper k -restraint r on G , there is a k -coloring c of G with c ( v )≠ r ( v ) for each vertex v of G . A graph G is amenable if it is amenably k -colorable and k is the chromatic number of G . For any k ≠3, there are infinitely many amenable k -critical graphs. For k ⩾ 3, we use a construction of B. Toft and amenable graphs to associate a k -colorable graph to any k -colorable finite hypergraph. Some constructions for amenable graphs are given. We also consider a related property—being strongly critical —that is satisfied by many critical graphs, including complete graphs. A strongly critical graph is critical and amenable, but the converse is not always true. The Dirac join operation preserves both amenability and the strongly critical property. In addition, the Hajos construction applied to a single edge in each of two strongly k -critical graphs yields an amenable graph. However, for any k ⩾5, there are amenable k -critical graphs for which the Hajos construction on two copies is not amenable.

title: The Ultimate Categorical Independence Ratio of a Graph
abstract: Let $\beta(G)$ denote the independence number of a graph $G$. We introduce $A(G) = \lim_{k \rightarrow \infty}\beta(G^{k})/|V(G)|^{k}$, where the categorical graph product is used. This limit, surprisingly, lies in the range $(0,1/2]\cup\{1\}$. We can show that this limit can take any such rational number, but is there any $G$ for which $A(G)$ is irrational? A useful technique for bounding $A(G)$ is to consider special spanning subgraphs. These bounds allow us to efficiently compute $A(G)$ for many $G$. We give a condition which if true for $G$ shows that $A(G)>\beta(G)/|V(G)|$. This brings up the question: for which $G$ does $A(G)=\beta(G)/|V(G)|$? This happens if $G$ is a Cayley graph of an Abelian group or if $G$ is a connected graph that has an automorphism which has a single orbit.

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: 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: Well-Covered Vector Spaces of Graphs
abstract: For any field ${\bf F}$, the set of all functions $f : V(G) \rightarrow {\bf F}$ whose sum on each maximal independent set is constant forms a vector space over ${\bf F}$. In this paper, we show that the dimension can vary depending on the characteristic of the field. We also investigate the dimensions of these vector spaces and show that while some families, such as chordal graphs, have unbounded dimension, other families, such as nonempty circulant graphs of prime order, have bounded dimension.

title: Plant snoRNA database
abstract: The Plant snoRNA database (http://www.scri.sari.ac.uk/plant_snoRNA/) provides information on small nucleolar RNAs from Arabidopsis and eighteen other plant species. Information includes sequences, expression data, methylation and pseudouridylation target modification sites, initial gene organization (polycistronic, single gene and intronic) and the number of gene variants. The Arabidopsis information is divided into box C/D and box H/ACA snoRNAs, and within each of these groups, by target sites in rRNA, snRNA or unknown. Alignments of orthologous genes and gene variants from different plant species are available for many snoRNA genes. Plant snoRNA genes have been given a standard nomenclature, designed wherever possible, to provide a consistent identity with yeast and human orthologues.

title: Why AM and Eurisko Appear to Work
abstract: Seven years ago, the AM program was constructed as an experiment in learning by discovery. Its source of power was a large body of heuristics, rules which guided it toward fruitful topics of investigation, toward profitable experiments to perform, toward plausible hypotheses and definitions. "Other heuristics evaluated those discoveries for utility and "interestingness", and they were added to AM's vocabulary of concepts. AM's ultimate limitation apparently was due to its inability to discover new, powerful, domain-specific heuristics for the various new fields it uncovered. At that time, it seemed straight-forward to simply add Heuretics (the study of heuristics) as one more field in which to let AM explore, observe, define, and develop. That task - learning new heuristics by discovery - turned out to be much more difficult than was realized initially, and we have just now achieved some successes at it. Along the way, it became clearer why AM had succeeded in the first place, and why it was so difficult to use the same paradigm to discover new heuristics. This paper discusses those recent insights. They spawn questions about "where the meaning really resides" in the concepts discovered by AM. This leads to an appreciation of the crucial and unique role of representation in theory formation, a role involving the relationship between Form and Content.

title: How laminar frontal cortex and basal ganglia circuits interact to control planned and reactive saccades
abstract: How does the brain learn to balance between reactive and planned behaviors? The basal ganglia (BG) and frontal cortex together allow animals to learn planned behaviors that acquire rewards when prepotent reactive behaviors are insufficient. This paper proposes a new model, called TELOS, to explain how laminar circuitry of the frontal cortex, exemplified by the frontal eye fields, interacts with the BG, thalamus, superior colliculus, and inferotemporal and parietal cortices to learn and perform reactive and planned eye movements. The model is formulated as fourteen computational hypotheses. These specify how strategy priming and action planning (in cortical layers III, Va and VI) are dissociated from movement execution (in layer Vb), how the BG help to choose among and gate competing plans, and how a visual stimulus may serve either as a movement target or as a discriminative cue to move elsewhere. The direct, indirect and hyperdirect pathways through the BG are shown to enable complex gating functions, including deferred execution of selected plans, and switching among alternative sensory-motor mappings. Notably, the model can learn and gate the use of a What-to-Where transformation that enables spatially invariant object representations to selectively excite spatially coded movement plans. Model simulations show how dopaminergic reward and non-reward signals guide monkeys to learn and perform saccadic eye movements in the fixation, single saccade, overlap, gap, and delay (memory-guided) saccade tasks. Model cell activation dynamics quantitatively simulate seventeen established types of dynamics exhibited by corresponding real cells during performance of these tasks.

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.

title: Computational and neural mechanisms of task switching
abstract: Switching between tasks that overlap in perceptual and response characteristics is assumed to rely upon the maintenance of task representations in prefrontal cortex (PFC). However, task-switching studies demonstrate ''switch costs,'' even when there is sufficient time to prepare for a new task. These costs suggest that task-switching performance reflects a complex interplay between priming and the updating and maintenance of task representations. We describe a computational model in which this interaction is made explicit and linked to the dynamics of PFC. Simulation results account for a variety of empirical phenomena and predict a double dissociation in lateral PFC that was subsequently identified.