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EULERIAN SUBGRAPH CONTAINING GIVEN VERTICES
, 2006
"... A vertex set S ⊆ V (G) is kweakedgeconnected if for every C ⊂ S and x ∈ S−C there are min{k, C} edgedisjoint (x, C)paths in G. For a graph G and a kweakedgeconnected vertex set S ⊂ V (G) with k ≥ 3 and 4 ≤ S  ≤ 2k, we show that G has an eulerian subgraph containing all vertices in S. ..."
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A vertex set S ⊆ V (G) is kweakedgeconnected if for every C ⊂ S and x ∈ S−C there are min{k, C} edgedisjoint (x, C)paths in G. For a graph G and a kweakedgeconnected vertex set S ⊂ V (G) with k ≥ 3 and 4 ≤ S  ≤ 2k, we show that G has an eulerian subgraph containing all vertices in S.
Frequent Subgraph Discovery
, 2001
"... Over the years, frequent itemset discovery algorithms have been used to solve various interesting problems. As data mining techniques are being increasingly applied to nontraditional domains, existing approaches for finding frequent itemsets cannot be used as they cannot model the requirement of th ..."
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Cited by 407 (14 self)
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of these domains. An alternate way of modeling the objects in these data sets, is to use a graph to model the database objects. Within that model, the problem of finding frequent patterns becomes that of discovering subgraphs that occur frequently over the entire set of graphs. In this paper we present a
Edge Detection
, 1985
"... For both biological systems and machines, vision begins with a large and unwieldy array of measurements of the amount of light reflected from surfaces in the environment. The goal of vision is to recover physical properties of objects in the scene, such as the location of object boundaries and the s ..."
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Cited by 1277 (1 self)
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about the physical properties of the scene are provided by the changes of intensity in the image. The importance of intensity changes and edges in early visual processg has led to extensive research on their detection, description and .use, both in computer and biological vision systems. This article
A combined corner and edge detector
 In Proc. of Fourth Alvey Vision Conference
, 1988
"... Consistency of image edge filtering is of prime importance for 3D interpretation of image sequences using feature tracking algorithms. To cater for image regions containing texture and isolated features, a combined corner and edge detector based on the local autocorrelation function is utilised, an ..."
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Cited by 2430 (2 self)
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Consistency of image edge filtering is of prime importance for 3D interpretation of image sequences using feature tracking algorithms. To cater for image regions containing texture and isolated features, a combined corner and edge detector based on the local autocorrelation function is utilised
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 512 (2 self)
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is to construct families of curves X, some singular, with pa(X)=g, over nonsingular parameter spaces, which in some sense contain enough singular curves to link together any two components that Mg might have. The essential thing that makes this method work now is a recent " stable reduction theorem "
A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
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Cited by 511 (8 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0
A computational approach to edge detection
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1986
"... AbstractThis paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal ..."
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Cited by 4621 (0 self)
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AbstractThis paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Inducing Features of Random Fields
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1997
"... We present a technique for constructing random fields from a set of training samples. The learning paradigm builds increasingly complex fields by allowing potential functions, or features, that are supported by increasingly large subgraphs. Each feature has a weight that is trained by minimizing the ..."
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Cited by 664 (14 self)
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We present a technique for constructing random fields from a set of training samples. The learning paradigm builds increasingly complex fields by allowing potential functions, or features, that are supported by increasingly large subgraphs. Each feature has a weight that is trained by minimizing
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