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Intersecting families of separated sets
 J. London Math. Soc
"... A set A ⊆ {1, 2,..., n} is said to be kseparated if, when considered on the circle, any two elements of A are separated by a gap of size at least k. We prove a conjecture due to Holroyd and Johnson [3],[4] that an analogue of the ErdősKoRado theorem holds for kseparated sets. In particular the r ..."
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Cited by 15 (2 self)
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A set A ⊆ {1, 2,..., n} is said to be kseparated if, when considered on the circle, any two elements of A are separated by a gap of size at least k. We prove a conjecture due to Holroyd and Johnson [3],[4] that an analogue of the ErdősKoRado theorem holds for kseparated sets. In particular
On the Bisectors of Weakly Separable Sets
, 2000
"... A bisector of two sets is the set of points equidistant to them. Bisectors arise naturally in several areas of computational geometry. We show that bisectors of weakly linearly separable sets in E d share many properties with separating lines. Among these, the bisector of a restricted class of line ..."
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A bisector of two sets is the set of points equidistant to them. Bisectors arise naturally in several areas of computational geometry. We show that bisectors of weakly linearly separable sets in E d share many properties with separating lines. Among these, the bisector of a restricted class
Connectivity and Separating Sets of Cages
 J. OF GRAPH THEORY
, 1998
"... A (k; g)cage is a graph of minimum order among kregular graphs with girth g. We show that for every cutset S of a (k; g)cage G, the induced subgraph G[S] has diameter at least bg=2c, with equality only when distance bg=2c occurs for at least two pairs of vertices in G[S]. This structural proper ..."
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Cited by 10 (1 self)
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A (k; g)cage is a graph of minimum order among kregular graphs with girth g. We show that for every cutset S of a (k; g)cage G, the induced subgraph G[S] has diameter at least bg=2c, with equality only when distance bg=2c occurs for at least two pairs of vertices in G[S]. This structural property is used to prove that every (k; g)cage with k 3 is 3connected. This result supports the conjecture of Fu, Huang, and Rodger that every (k; g)cage is kconnected. A nonseparating gcycle C in a graph G is a cycle of length g such that G − V (C) is connected. We prove that every (k; g)cage contains a nonseparating gcycle. For even g, we prove that every gcycle in a (k; g)cage is nonseparating.
Equivariant Adaptive Source Separation
 IEEE Trans. on Signal Processing
, 1996
"... Source separation consists in recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation which implements an adaptive version of equivariant estimation and is henceforth called EASI (Eq ..."
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Cited by 449 (9 self)
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Source separation consists in recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation which implements an adaptive version of equivariant estimation and is henceforth called EASI
A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which ..."
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Cited by 461 (1 self)
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Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which
Minimal Separating Sets for Muller Automata
, 1997
"... For a Muller automaton only a subset of its states is needed to decide whether a run is accepting or not: The set I the infinitely often visited states can be replaced by the intersection I " W with a fixed set W of states, provided W is large enough to distinguish between accepting and nonacc ..."
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accepting loops in the automaton. We call such a subset W a separating set. Whereas the idea was previously introduced by McNaughton [McN93], the algorithmic construction of smallest separating sets is not treated in the literature. In this paper we show that the test whether in a Muller automaton a separating
Performance Optimization Using Separator Sets
"... In this paper, we propose a new method to optimize a performance of a very large circuit. We find the best set of local transformations to be applied to the circuit, by inserting “padding nodes ” on noncritical edges of the circuit, and calculating separator sets of the circuit using separator sets ..."
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Cited by 1 (0 self)
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In this paper, we propose a new method to optimize a performance of a very large circuit. We find the best set of local transformations to be applied to the circuit, by inserting “padding nodes ” on noncritical edges of the circuit, and calculating separator sets of the circuit using separator
Identification of Prokaryotic and Eukaryotic Signal Peptides and Prediction of Their Cleavage Sites
, 1997
"... We have developed a new method for identification of signal peptides and their cleavage sites based on neural networks trained on separate sets of prokaryotic and eukaryotic sequences. The method performs significantly better than previous prediction schemes, and can easily be applied on genomewide ..."
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Cited by 787 (17 self)
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We have developed a new method for identification of signal peptides and their cleavage sites based on neural networks trained on separate sets of prokaryotic and eukaryotic sequences. The method performs significantly better than previous prediction schemes, and can easily be applied on genome
Thesis Proposal: Separating Sets for Finite Groups
, 2003
"... For my thesis, I will investigate separating sets for finite groups. The goal will be to research methods for finding minimal separating sets for a finite group. ..."
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For my thesis, I will investigate separating sets for finite groups. The goal will be to research methods for finding minimal separating sets for a finite group.
Results 1  10
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24,727