18896340
On the Roots of Chromatic Polynomials
It is proved that the chromatic polynomial of a connected graph with n vertices and m edges has a root with modulus at least (m?1)/(n?2); this bound is best possible for trees and 2-trees (only). It is also proved that the chromatic polynomial of a graph with few triangles that is not a forest has a nonreal root and that there is a graph with n vertices whose chromatic polynomial has a root with imaginary part greater thann/4.
28649866
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 .
14976506
Average independence polynomials
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.
2327812
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.
40600226
The Complexity of Generalized Graph Colorings
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.
5392880
On chromatic roots with negative real part
5243593
Steps Toward Automatic Theory Formation
This paper describes a theory formation system which can discover a partial axiomization of a data base represented as extensionally defined binary relations.- The system first discovers all possible intensional definitions of each binary relation in terms of the others. It then determines a minimal set of these relations from which the others can be defined. It then attempts to discover all the ways the relations of this minimal set can interact with each other, thus generating a set of inference rules. Although the system was originally designed to explore automatic techniques for theory construction for question-answering systems, it is currently being expanded to function as a symbiotic system to help social scientists explore certain kinds of data bases.
7956229
How laminar frontal cortex and basal ganglia circuits interact to control planned and reactive saccades
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.
45989851
The Social Life of Documents
Documents are evolving as means for structuring and navigating information space, and resources for constructing and negotiating social space
7379001
The ribonuclease P database
The Ribonuclease P Sequence database is a compilation of RNase P sequences, sequence alignments, secondary structures, three-dimensional models, and accessory information. In its initial form, the database contains information on RNase P RNA in bacteria and archaea, and RNase P protein in bacteria. The sequences themselves are presented phylogenetically ordered and aligned. The database also contains secondary structures of bacterial and archaeal RNAs, including specially annotated 'reference' secondary structures of Escherichia coli and Bacillus subtilis RNase P RNAs, a minimum phylogenetic consensus structure, and coordinates for models of three-dimensional structure.
27879633
To dream the invisible dream
often credited as the creator of the computer game industry, explores the “Relationships between Fun and the Computer Business.” In his article he reminisces, assesses, and projects the effects from the game industry to the computer industry as a whole. Bushnell’s article makes tangible some of the incredible distance we’ve come since the 1970s—from a world where manufacturers didn’t take cathode-ray tube use in the computer industry seriously to a time when most two-year-old children know about computers. Bushnell’s way is to mix lessons learned from the game industry with some as-yet unexplored visions of the way we will play. Henry Lieberman’s work has been that of creating programming and idea presentation environments using his favorite tools of creation objects (his work on actors), dynamic languages (his work on garbage collection), and interactive environments (his work on programming by example). Lieberman’s article, “Intelligent Graphics,” focuses on the inventive serendipity that has and can come out of the relationship between AI and graphics—an idea promoted by yet another pioneer, Muriel Cooper. He also briefly discusses programming by example, a style of interaction that he has been working to demonstrate and promote over the last couple of decades. Ken Kahn also cares deeply about programming languages, having devoted his research career to creating Prolog interpreters, parallel logic systems, and logic-oriented systems. In his article, we see him engaged in his first love, that of creating visual approaches for thinking about programs. Watching programs execute, seeing their structure, seeing their function, organizing them—all with the underlying goal of making programming as easy as child’s play. Finally, as you look to my article, you see me not working or talking about any one idea as I could, but giving a review with some context that describes many of the ideas shaping the way people are using computers today. I hope this eclectic collection of articles can serve as a celebration of our temptations to explore and design the ways computers will help us communicate, create, and record our experiences.