Results 1  10
of
10
The Computational Support of Scientific Discovery
, 2000
"... In this paper, we review AI research on computational discovery and its recent application to the discovery of new scientific knowledge. We characterize five historical stages of the scientific discovery process, which we use as an organizational framework in describing applications. We also identif ..."
Abstract

Cited by 35 (3 self)
 Add to MetaCart
In this paper, we review AI research on computational discovery and its recent application to the discovery of new scientific knowledge. We characterize five historical stages of the scientific discovery process, which we use as an organizational framework in describing applications. We also identify five distinct steps during which developers or users can influence the behavior of a computational discovery system. Rather than criticizing such intervention, as done in the past, we recommend it as the preferred approach to using discovery software. As evidence for the advantages of such humancomputer cooperation, we report seven examples of novel, computeraided discoveries that have appeared in the scientific literature. We consider briefly the role that humans played in each case, then examine one such interaction in more detail. We close by recommending that future systems provide more explicit support for human intervention in the discovery process. Running head: Computational Sci...
The ComputerAided Discovery of Scientific Knowledge
 In Proceedings of the first international conference on discovery science
, 1998
"... . In this paper, we review AI research on computational discovery and its recent application to the discovery of new scientific knowledge. We characterize five historical stages of the scientific discovery process, which we use as an organizational framework in describing applications. We also ident ..."
Abstract

Cited by 25 (2 self)
 Add to MetaCart
(Show Context)
. In this paper, we review AI research on computational discovery and its recent application to the discovery of new scientific knowledge. We characterize five historical stages of the scientific discovery process, which we use as an organizational framework in describing applications. We also identify five distinct steps during which developers or users can influence the behavior of a computational discovery system. Rather than criticizing such intervention, as done in the past, we recommend it as the preferred approach to using discovery software. As evidence for the advantages of such humancomputer cooperation, we report seven examples of novel, computeraided discoveries that have appeared in the scientific literature, along with the role that humans played in each case. We close by recommending that future systems provide more explicit support for human intervention in the discovery process. 1 Introduction The process of scientific discovery has long been viewed as the pinnacle ...
Toward Fully Automated Fragments of Graph Theory, Graph Theory Notes of New York XLII
 C. E. LARSON
, 2002
"... Abstract. We continue the discussion of three topics initiated in the first part of this paper starting with mathematical aspects of the machine intelligence debate initiated in the books of Roger Penrose. Stability Sorting Patterns are byproducts of Minuteman, a fullerene version of Graffiti which ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
Abstract. We continue the discussion of three topics initiated in the first part of this paper starting with mathematical aspects of the machine intelligence debate initiated in the books of Roger Penrose. Stability Sorting Patterns are byproducts of Minuteman, a fullerene version of Graffiti which led to the discovery of a new representation and characterization of the icosahedral C60. Some of the conjectures of Minuteman postulate new properties of stable fullerenes and possibly other materials. We discuss here in greater detail two interpretations of one of the conjectures of Minuteman, one of which was incorrectly claimed to be refuted and the other one, which in spite of being refuted, presumably is approximately correct, suggesting that stable fullerenes tend to have very large separators. Red Burton is a new implementation of Graffiti to teach mathematics Texas style, i.e., by the process of selfdiscovery. This version and particularly its offshoot, Little Red Riding Hood, are suitable for using the program in an almost fully automated manner. Twas brillig, and the slighty toves Did gyre and gimble in the wabe: All mimsy were the borogoves. And the mome raths outgrabe.
Computers and Discovery in Algebraic Graph Theory
 Edinburgh, 2001), Linear Algebra Appl
, 2001
"... We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory. ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory.
Spanning Trees with Many Leaves and Average Distance
"... In this paper we prove several new lower bounds on the maximum number of leaves of a spanning tree of a graph related to its order, independence number, local independence number, and the maximum order of a bipartite subgraph. These new lower bounds were conjectured by the program Graffiti.pc, a var ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
In this paper we prove several new lower bounds on the maximum number of leaves of a spanning tree of a graph related to its order, independence number, local independence number, and the maximum order of a bipartite subgraph. These new lower bounds were conjectured by the program Graffiti.pc, a variant of the program Graffiti. We use two of these results to give two partial resolutions of conjecture 747 of Graffiti (circa 1992), which states that the average distance of a graph is not more than half the maximum order of an induced bipartite subgraph. If correct, this conjecture would generalize conjecture number 2 of Graffiti, which states that the average distance is not more than the independence number. Conjecture number 2 was first proved by F. Chung. In particular, we show that the average distance is less than half the maximum order of a bipartite subgraph, plus onehalf; we also show that if the local independence number is at least five, then the average distance is less than half the maximum order of a bipartite subgraph. In conclusion, we give some open problems related to average distance or the maximum number of leaves
Some History of the Development of Graffiti
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science 69: Graphs and Discovery
"... Abstract. This paper provides some history of the development of the conjecture ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract. This paper provides some history of the development of the conjecture
The ComputerAided Discovery of Scientic Knowledge
"... Abstract. In this paper, we review AI research on computational discovery and its recent application to the discovery of new scientic knowledge. We characterize ve historical stages of the scientic discovery process, which we use as an organizational framework in describing applications. We also ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper, we review AI research on computational discovery and its recent application to the discovery of new scientic knowledge. We characterize ve historical stages of the scientic discovery process, which we use as an organizational framework in describing applications. We also identify ve distinct steps during which developers or users can in
uence the behavior of a computational discovery system. Rather than criticizing such intervention, as done in the past, we recommend it as the preferred approach to using discovery software. As evidence for the advantages of such humancomputer cooperation, we report seven examples of novel, computeraided discoveries that have appeared in the scienti c literature, along with the role that humans played in each case. We close by recommending that future systems provide more explicit support for human intervention in the discovery process. 1
LOWER BOUNDS FOR THE DOMINATION NUMBER
"... Abstract. In this note, we prove several lower bounds on the domination number of simple connected graphs. Among these are the following: the domination number is at least twothirds of the radius of the graph, three times the domination number is at least two more than the number of cutvertices in ..."
Abstract
 Add to MetaCart
Abstract. In this note, we prove several lower bounds on the domination number of simple connected graphs. Among these are the following: the domination number is at least twothirds of the radius of the graph, three times the domination number is at least two more than the number of cutvertices in the graph, and the domination number of a tree is at least as large as the minimum order of a maximal matching.
A NOTE ON DOMINATING SETS AND AVERAGE DISTANCE
"... Abstract. We show that the total domination number of a simple connected graph is greater than the average distance of the graph minus onehalf, and that this inequality is best possible. In addition, we show that the domination number of the graph is greater than twothirds of the average distance ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We show that the total domination number of a simple connected graph is greater than the average distance of the graph minus onehalf, and that this inequality is best possible. In addition, we show that the domination number of the graph is greater than twothirds of the average distance minus onethird, and that this inequality is best possible. Although the latter inequality is a corollary to a result of P. Dankelmann, we present a short and direct proof.