2058234
Subdivisions and Chromatic Roots
It is well known that chromatic polynomials can have roots (chromatic roots) of arbitrarily large modulus. We prove here that for any graph G and any ?>0, there is a subdivision of G all of whose chromatic roots lie in |z?1|<1+?.
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.
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.
5392880
On chromatic roots with negative real part
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.
44284809
The strongly connected reliability of complete digraphs
Given a digraph D, consider the model where each vertex is always operational, but the edges are independently operational with probability p. The strongly connected reliability of D, scRel(D, p), is the probability that the spanning subgraph of D consisting of the operational edges is strongly connected. One can view strongly connected reliability as the probability that any vertex can send information to any other vertex, given that edges fail independently. ∗Partially supported by a grant from NSERC. Communicating author.
267100
Proximity-aware directory-based coherence for multi-core processor architectures
As the number of cores increases on chip multiprocessors, coherence is fast becoming a central issue for multi-core performance. This is exacerbated by the fact that interconnection speeds are not scaling well with technology. This paper describes mechanisms to accelerate coherence for a multi-core architecture that has multiple private L2 caches and a scalable point-to-point interconnect between cores. These techniques exploit the differences in geometry between chip multiprocessors and traditional multiprocessor architectures.
 Directory-based protocols have been proposed as a scalable alternative to snoop-based protocols. In this paper, we discuss implementations of coherence for CMPs and propose and evaluate a novel directory-based coherence scheme to improve the performance of parallel programs on such processors. Proximity-aware coherence accelerates read and write misses by initiating cache-to-cache transfers from the spatially closest sharer. This has the dual benefit of eliminating unnecessary accesses to off-chip memory, and minimizing the distance over which communicated data moves across the network. The proposed schemes result in speedups up to 74.9% for our workloads.
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.
1800673
Why AM and Eurisko Appear to Work
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.
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.
38979633
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.