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Study of the average size of . . . Automata
, 2011
"... In this paper, the relation between the Glushkov automaton (Apos) and the partial derivative automaton (Apd) of a given regular expression, in terms of transition complexity, is studied. The average transition complexity of Apos was proved by Nicaud to be linear in the size of the corresponding expr ..."
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In this paper, the relation between the Glushkov automaton (Apos) and the partial derivative automaton (Apd) of a given regular expression, in terms of transition complexity, is studied. The average transition complexity of Apos was proved by Nicaud to be linear in the size of the corresponding
The average size of ordered binary subgraphs t
"... To analyse the demands made on the garbage collector in a graph reduction system, the change in size of an average graph is studied when an arbitrary edge is removed. In ordered binary trees the average number of deleted nodes as a result of cutting a single edge is equal to the average size of a su ..."
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To analyse the demands made on the garbage collector in a graph reduction system, the change in size of an average graph is studied when an arbitrary edge is removed. In ordered binary trees the average number of deleted nodes as a result of cutting a single edge is equal to the average size of a
An Upper Bound on the Average Size of Silhouettes
 in &quot;22nd ACM Symposium on Computational Geometry 2006
, 2006
"... It is a widely observed phenomenon in computer graphics that the size of the silhouette of a polyhedron is much smaller than the size of the whole polyhedron. This paper provides, for the first time, theoretical evidence supporting this for a large class of objects, namely for polyhedra that approxi ..."
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Cited by 6 (1 self)
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that approximate surfaces in some reasonable way; the surfaces may be nonconvex and nondifferentiable and they may have boundaries. We prove that such polyhedra have silhouettes of expected size O ( √ n) where the average is taken over all points of view and n is the complexity of the polyhedron. 1
On the Average Size of PD . . . Combinatorics Approach
, 2010
"... The partial derivative automaton (Apd) is usually smaller than other nondeterministic finite automata constructed from a regular expression, and it can be seen as a quotient of the Glushkov automaton (Apos). By estimating the number of regular expressions that have ε as a partial derivative, we com ..."
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compute a lower bound of the average number of mergings of states in Apos and describe its asymptotic behaviour. This depends on the alphabet size, k, and its limit, as k goes to infinity, is 1. The lower bound corresponds 2 exactly to consider the Apd automaton for the marked version of the regular
Average size of unstretched RemoteSpanners
, 2008
"... Motivated by the optimization of link state routing in ad hoc networks, and the concept of multipoint relays, we introduce the notion of remotespanner. Given an unweighted graph G, a remote spanner is a set of links H such that for any pair of nodes (u, v) there exists a shortest path in G for whic ..."
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Cited by 2 (1 self)
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Motivated by the optimization of link state routing in ad hoc networks, and the concept of multipoint relays, we introduce the notion of remotespanner. Given an unweighted graph G, a remote spanner is a set of links H such that for any pair of nodes (u, v) there exists a shortest path in G for which all links in the path that are not adjacent to u belong to H. The remote spanner is a kind of minimal topology information beyond its neighborhood that any node would need in order to compute its shortest paths in a distributed way. This can be extended to kconnected graphs by considering minimum length sum over k disjoint paths as distance. In this paper, we give distributed algorithms for computing remotespanners in order to obtain sparse remotespanners with various properties. We provide a polynomial distributed algorithm that computes a kconnecting unstretched remotespanner whose number of edges is at a factor 2(1 + log ∆) from optimal where ∆ is the maximum degree of a node. Interestingly, its expected compression ratio in number of edges is O ( k n log n) in ErdösRényi graph model and O( ( k 2 n) 3) in the unit disk graph model with a uniform Poisson distribution of nodes. 1
The relationship between return and market value of common stocks
 Journal of Financial Economics
, 1981
"... This study examines the empirical relattonship between the return and the total market value of NYSE common stocks. It is found that smaller firms have had htgher risk adjusted returns, on average, than larger lirms. This ‘size effect ’ has been in existence for at least forty years and is evidence ..."
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Cited by 791 (0 self)
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This study examines the empirical relattonship between the return and the total market value of NYSE common stocks. It is found that smaller firms have had htgher risk adjusted returns, on average, than larger lirms. This ‘size effect ’ has been in existence for at least forty years and is evidence
The Declining Average Size of Establishments: Evidence and Explanations
, 2011
"... this paper. The views expressed in this paper are solely those of the authors and do not necessarily reflect the Keen observers of labor market statistics have noticed that the average size of establishments has been decreasing during the last decade. The graph immediately below presents the average ..."
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Cited by 4 (1 self)
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this paper. The views expressed in this paper are solely those of the authors and do not necessarily reflect the Keen observers of labor market statistics have noticed that the average size of establishments has been decreasing during the last decade. The graph immediately below presents
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