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Deterministic and Stochastic Models for Coalescence (Aggregation, Coagulation): a Review of the MeanField Theory for Probabilists
 Bernoulli
, 1997
"... Consider N particles, which merge into clusters according to the rule: a cluster of size x and a cluster of size y merge at (stochastic) rate K(x; y)=N , where K is a specified rate kernel. This MarcusLushnikov model of stochastic coalescence, and the underlying deterministic approximation given by ..."
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Cited by 222 (13 self)
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are only now starting to be studied rigorously, so many interesting open problems appear. Keywords. branching process, coalescence, continuum tree, densitydependent Markov process, gelation, random graph, random tree, Smoluchowski coagulation equation Research supported by N.S.F. Grant DMS9622859 1
On the Critical Value for "Percolation" of MinimumWeight Trees in the MeanField Distance Model
, 1996
"... Consider the complete ngraph with independent exponential (mean n) edgeweights. Let M (c; n) be the maximal size of subtree for which the average edgeweight is at most c. It is shown that M (c; n) transitions from o(n) to \Omega\Gamma n) around some critical value c(0), which can be specified ..."
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Cited by 4 (1 self)
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be specified in terms of a fixed point of a mapping on probability distributions. Research supported by N.S.F. Grant DMS9622859 1 1 Introduction To each edge e of the complete graph on f1; 2; : : : ; ng attach a weight w e , where the (w e ) are independent exponential (mean n) r.v.'s. Call
The Percolation Process on a Tree Where Infinite Clusters are Frozen
 Math. Proc. Cambridge Philos. Soc
, 1999
"... Modify the usual percolation process on the infinite binary tree by forbidding infinite clusters to grow further. The ultimate configuration will consist of both infinite and finite clusters. We give a rigorous construction of a version of this process and show that one can do explicit calculations ..."
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Cited by 24 (2 self)
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cluster on the tree. Similarly, a typical finite cluster at each time t ? 1=2 has the distribution of a critical percolation cluster. This elaborates an observation of Stockmayer (1942). AMS 1991 subject classification: 60K35, 05C80 Research supported by N.S.F. Grant DMS9622859 1 Introduction Let
Mixing Time for a Markov Chain on Cladograms
 Combin. Probab. Comput
, 1998
"... A cladogram is a tree with labeled leaves and unlabeled degree3 branchpoints. A certain Markov chain on the set of nleaf cladograms consists of removing a random leaf (and its incident edge) and reattaching it to a random edge. We show that the mixing time (time to approach the uniform stationary ..."
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Cited by 13 (0 self)
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distribution) for this chain is at least O(n 2 ) and at most O(n 3 ). AMS 1991 subject classification: 05C05, 60C05, 60J10. Key words and phrases. Coupling, Markov chain, Markov chain Monte Carlo, mixing time, phylogenetic tree. Research supported by N.S.F. Grant DMS9622859 1 Introduction
Emergence of the Giant Component in Special MarcusLushnikov Processes
 Random Structures and Algorithms
, 1997
"... Component sizes in the usual random graph process are a special case of the MarcusLushnikov process discussed in the scientific literature, so it is natural to ask how theory surrounding emergence of the giant component generalizes to the MarcusLushnikov process. Essentially no rigorous results ar ..."
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Cited by 14 (4 self)
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for each pair of clusters, of sizes fx; yg say, they coalesce into a single cluster of size x + y at rate K(x; y)=n where K(x; y) = K(y; x) 0 is some specified rate kernel. This rule specifies a continuoustime finitestate Markov process which we shall call the Research supported by N.S.F. Grant DMS
Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I
, 1960
"... this paper in L a T E Xpartly supported by ARPA (ONR) grant N000149410775 to Stanford University where John McCarthy has been since 1962. Copied with minor notational changes from CACM, April 1960. If you want the exact typography, look there. Current address, John McCarthy, Computer Science Depa ..."
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Cited by 452 (3 self)
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this paper in L a T E Xpartly supported by ARPA (ONR) grant N000149410775 to Stanford University where John McCarthy has been since 1962. Copied with minor notational changes from CACM, April 1960. If you want the exact typography, look there. Current address, John McCarthy, Computer Science
On visible surface generation by a priori tree structures
 Computer Graphics
, 1980
"... This paper describes a new algorithm for solving the hidden surface (or line) problem, to more rapidly generate realistic images of 3D scenes composed of polygons, and presents the development of theoretical foundations in the area as well as additional related algorithms. As in many applications t ..."
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Cited by 370 (6 self)
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specifying parameters zor an image (using knobs, switches, or cockpit controls) and the *This research was partially supported by NSF under Grants MCS7900168 and MC57902593, and was zacilitated by the use of
SelfTesting/Correcting with Applications to Numerical Problems
, 1990
"... Suppose someone gives us an extremely fast program P that we can call as a black box to compute a function f . Should we trust that P works correctly? A selftesting/correcting pair allows us to: (1) estimate the probability that P (x) 6= f(x) when x is randomly chosen; (2) on any input x, compute ..."
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Cited by 357 (27 self)
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f(x) correctly as long as P is not too faulty on average. Furthermore, both (1) and (2) take time only slightly more than Computer Science Division, U.C. Berkeley, Berkeley, California 94720, Supported by NSF Grant No. CCR 8813632. y International Computer Science Institute, Berkeley
A model for Pavlovian learning: Variations in the effectiveness of conditioned but not of unconditioned stimuli
 Psychological Review
, 1980
"... Several formal models of excitatory classical conditioning are reviewed. It is suggested that a central problem for all of them is the explanation of cases in which learning does not occur in spite of the fact that the conditioned stimulus is a signal for the reinforcer. We propose a new model that ..."
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Cited by 286 (10 self)
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. Bailey, S. Channel!, N. Mackintosh, and E. Macphail for their comments on earlier versions of this article. Requests for reprints should be sent to John Pearce,
Objects and Views
 ACM SIGMOD INTERNATIONAL CONFERENCE ON MANAGEMENT OF DATA
, 1991
"... Objectoriented databases have been introduced primarily to ease the development of database applications. However, the difficulties encountered when, for instance, trying to restructure data or integrate databases demonstrate that the models being used still lack flexibility. We claim that the natu ..."
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Cited by 258 (9 self)
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Objectoriented databases have been introduced primarily to ease the development of database applications. However, the difficulties encountered when, for instance, trying to restructure data or integrate databases demonstrate that the models being used still lack flexibility. We claim that the natural way to overcome these shortcomings is to introduce a sophisticated view mechanism. This paper presents such a mechanism, one which allows a programmer to restructure the class hierarchy and modify the behavior and structure of objects. The mechanism allows a programmer to specify attribute values implicitly, rather than storing them. It also allows him to introduce new classes into the class hierarchy. These virtual classes are populated by selecting existing objects from other classes and by creating new objects. Fixing the identify of new objects during database updates introduces subtle issues into view design. Our presentation, mostly informal, leans on a number of illustrative examples meant to emphasize the simplicity of our mechanism. 1
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