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wanyu
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Task Categories:
conditionaltextgeneration
Languages:
enUS
Multilinguality:
monolingual
Language Creators:
found
Annotations Creators:
crowdsourced
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original
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(2) There never are more than 2n steady states ;
 (2) there never are more than 2n steady states ;
 <fluency> This note studies the number of positive steady states in biomolecular reactions consisting of activation/deactivation futile cycles, such as those arising from phosphorylations and dephosphorylations at each level of a MAPK cascade. It is shown that (1) for some parameter ranges, there are at least n+1 (if n is even) or n (if n is odd) steady states; <S> (2) There never are more than 2n steady states ; </S> (3) for parameters near the standard MichaelisMenten quasisteady state conditions, there are at most n+1 steady states; and (4) for parameters far from the standard MichaelisMenten quasisteady state conditions, there is at most one steady state.
 fluency
 0.99913883
 0704.0036
 1

This philosophical paper discusses the benefits of describing the world as information, especially in the study of the evolution of life and cognition.
 This paper discusses the benefits of describing the world as information, especially in the study of the evolution of life and cognition.
 <clarity> <S> This philosophical paper discusses the benefits of describing the world as information, especially in the study of the evolution of life and cognition. </S> Traditional studies encounter difficulties because it is difficult to describe life and cognition in terms of matter and energy, falling into a dualist trap . However, if matter and energy, as well as life and cognition, are described in terms of information, evolution can be described consistently as information becoming more complex.
 clarity
 0.9986959
 0704.0304
 1

Traditional studies encounter difficulties because it is difficult to describe life and cognition in terms of matter and energy, falling into a dualist trap .
 Traditional studies encounter problems because it is difficult to describe life and cognition in terms of matter and energy, falling into a dualist trap .
 <coherence> This philosophical paper discusses the benefits of describing the world as information, especially in the study of the evolution of life and cognition. <S> Traditional studies encounter difficulties because it is difficult to describe life and cognition in terms of matter and energy, falling into a dualist trap . </S> However, if matter and energy, as well as life and cognition, are described in terms of information, evolution can be described consistently as information becoming more complex. Moreover, information theory is already well established and formalized.
 coherence
 0.6070667
 0704.0304
 1

Moreover, information theory is already well established and formalized.
 <coherence> Traditional studies encounter difficulties because it is difficult to describe life and cognition in terms of matter and energy, falling into a dualist trap . However, if matter and energy, as well as life and cognition, are described in terms of information, evolution can be described consistently as information becoming more complex. <S> Moreover, information theory is already well established and formalized. </S> The paper presents five tentative laws of information, which are generalizations of Darwinian, cybernetic, thermodynamic, and complexity principles. These are further used to discuss the notions of life and cognition , including their origins and evolution.
 coherence
 0.99856454
 0704.0304
 1


These are further used to discuss the notions of life and cognition , including their origins and evolution.
 These are further used to discuss the notions of life and cognition and their evolution.
 <clarity> Moreover, information theory is already well established and formalized. The paper presents five tentative laws of information, which are generalizations of Darwinian, cybernetic, thermodynamic, and complexity principles. <S> These are further used to discuss the notions of life and cognition , including their origins and evolution. </S>
 clarity
 0.9989242
 0704.0304
 1

These are further used to discuss the notions of life and cognition and their evolution.
 These are further used to discuss the notions of life , cognition and their evolution.
 <fluency> However, if matter and energy, as well as life and cognition, are described in terms of information, evolution can be described consistently as information becoming more complex. The paper presents five tentative laws of information, valid at multiple scales, which are generalizations of Darwinian, cybernetic, thermodynamic, and complexity principles. <S> These are further used to discuss the notions of life and cognition and their evolution. </S>
 fluency
 0.9991115
 0704.0304
 2

The incidence matrix of C_{nm} of a simple digraph is mapped into a incidence matrix F of a balanced bipartite undirected graph by divided C into two groups.
 The incidence matrix of C_{nm} of a simple digraph to a matrix F of a balanced bipartite undirected graph by divided C into two groups.
 <clarity> <S> The incidence matrix of C_{nm} of a simple digraph is mapped into a incidence matrix F of a balanced bipartite undirected graph by divided C into two groups. </S> Based on the mapping , it proves that the complexity is polynomial to determin a Hamiltonian cycle existence or not in a simple digraph with degree bound two and obtain all solution if it exists Hamiltonian cycle. It also proves P= NP with the different resultsin \mbox{ PLESNIK1978 .
 clarity
 0.9991511
 0704.0309
 1

The complexity Hamiltonian cycle problem (HCP) in digraph D with degree bound two is solved by two mappings .
 The Hamiltonian cycle problem (HCP) in digraph D with degree bound two is solved by two mappings .
 <clarity> <S> The complexity Hamiltonian cycle problem (HCP) in digraph D with degree bound two is solved by two mappings . </S> The first bijection is between of a incidence matrix of C_{nm} of a simple digraph to a matrix F of a balanced bipartite undirected graph G; The second mapping is reverse from a perfect matching of G to a cycle of D.
 clarity
 0.99172664
 0704.0309
 2

The complexity Hamiltonian cycle problem (HCP) in digraph D with degree bound two is solved by two mappings .
 The complexity Hamiltonian cycle problem (HCP) in digraphs D with degree bound two is solved by two mappings .
 <fluency> <S> The complexity Hamiltonian cycle problem (HCP) in digraph D with degree bound two is solved by two mappings . </S> The first bijection is between of a incidence matrix of C_{nm} of a simple digraph to a matrix F of a balanced bipartite undirected graph G; The second mapping is reverse from a perfect matching of G to a cycle of D.
 fluency
 0.99900913
 0704.0309
 2

The first bijection is between of a incidence matrix of C_{nm} of a simple digraph to a matrix F of a balanced bipartite undirected graph G;
 The first bijection is between an incidence matrix C_{nm} of a simple digraph to a matrix F of a balanced bipartite undirected graph G;
 <fluency> The complexity Hamiltonian cycle problem (HCP) in digraph D with degree bound two is solved by two mappings . <S> The first bijection is between of a incidence matrix of C_{nm} of a simple digraph to a matrix F of a balanced bipartite undirected graph G; </S> The second mapping is reverse from a perfect matching of G to a cycle of D. It proves that the complexity of HCP in D is polynomial . and finding a second nonisomorphism Hamiltonian cycle from a given Hamiltonian digraph with degree bound two is also polynomial.
 fluency
 0.97384065
 0704.0309
 2

The first bijection is between of a incidence matrix of C_{nm} of a simple digraph to a matrix F of a balanced bipartite undirected graph G;
 The first bijection is between of a incidence matrix of C_{nm} of simple digraph and an incidence matrix F of a balanced bipartite undirected graph G;
 <clarity> The complexity Hamiltonian cycle problem (HCP) in digraph D with degree bound two is solved by two mappings . <S> The first bijection is between of a incidence matrix of C_{nm} of a simple digraph to a matrix F of a balanced bipartite undirected graph G; </S> The second mapping is reverse from a perfect matching of G to a cycle of D. It proves that the complexity of HCP in D is polynomial . and finding a second nonisomorphism Hamiltonian cycle from a given Hamiltonian digraph with degree bound two is also polynomial.
 clarity
 0.65584946
 0704.0309
 2

The first bijection is between of a incidence matrix of C_{nm} of a simple digraph to a matrix F of a balanced bipartite undirected graph G;
 The first bijection is between of a incidence matrix of C_{nm} of a simple digraph to a matrix F of balanced bipartite undirected graph G;
 <fluency> The complexity Hamiltonian cycle problem (HCP) in digraph D with degree bound two is solved by two mappings . <S> The first bijection is between of a incidence matrix of C_{nm} of a simple digraph to a matrix F of a balanced bipartite undirected graph G; </S> The second mapping is reverse from a perfect matching of G to a cycle of D. It proves that the complexity of HCP in D is polynomial . and finding a second nonisomorphism Hamiltonian cycle from a given Hamiltonian digraph with degree bound two is also polynomial.
 fluency
 0.99912816
 0704.0309
 2

The second mapping is reverse from a perfect matching of G to a cycle of D.
 The second mapping is from a perfect matching of G to a cycle of D.
 <clarity> The complexity Hamiltonian cycle problem (HCP) in digraph D with degree bound two is solved by two mappings . The first bijection is between of a incidence matrix of C_{nm} of a simple digraph to a matrix F of a balanced bipartite undirected graph G; <S> The second mapping is reverse from a perfect matching of G to a cycle of D. </S> It proves that the complexity of HCP in D is polynomial . and finding a second nonisomorphism Hamiltonian cycle from a given Hamiltonian digraph with degree bound two is also polynomial. Lastly it deduce P=BPP =NP base on the results.
 clarity
 0.99844223
 0704.0309
 2

It proves that the complexity of HCP in D is polynomial . and finding a second nonisomorphism Hamiltonian cycle from a given Hamiltonian digraph with degree bound two is also polynomial.
 It proves that the complexity of HCP in D is polynomial , and finding a second nonisomorphism Hamiltonian cycle from a given Hamiltonian digraph with degree bound two is also polynomial.
 <fluency> The first bijection is between of a incidence matrix of C_{nm} of a simple digraph to a matrix F of a balanced bipartite undirected graph G; The second mapping is reverse from a perfect matching of G to a cycle of D. <S> It proves that the complexity of HCP in D is polynomial . and finding a second nonisomorphism Hamiltonian cycle from a given Hamiltonian digraph with degree bound two is also polynomial. </S> Lastly it deduce P=BPP =NP base on the results.
 fluency
 0.9990652
 0704.0309
 2

We build a sequence of empirical measures on the space D(R_+,R^d) of R^dvalued c \`a%DIFDELCMD < }%%% dl \`a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^dvalued Markov and Feller process (X_t).
 We build a sequence of empirical measures on the space D(R_+,R^d) of R^dvalued \`a%DIFDELCMD < }%%% dl \`a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^dvalued Markov and Feller process (X_t).
 <clarity> <S> We build a sequence of empirical measures on the space D(R_+,R^d) of R^dvalued c \`a%DIFDELCMD < }%%% dl \`a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^dvalued Markov and Feller process (X_t). </S> We obtain some general results of convergence of this sequence. Then, we apply them to Brownian diffusions and solutions to L \'e%DIFDELCMD < }%%% vy driven SDE's under some Lyapunovtype stability assumptions.
 clarity
 0.9913898
 0704.0335
 1

We build a sequence of empirical measures on the space D(R_+,R^d) of R^dvalued c \`a%DIFDELCMD < }%%% dl \`a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^dvalued Markov and Feller process (X_t).
 We build a sequence of empirical measures on the space D(R_+,R^d) of R^dvalued c %DIFDELCMD < }%%% dl \`a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^dvalued Markov and Feller process (X_t).
 <fluency> <S> We build a sequence of empirical measures on the space D(R_+,R^d) of R^dvalued c \`a%DIFDELCMD < }%%% dl \`a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^dvalued Markov and Feller process (X_t). </S> We obtain some general results of convergence of this sequence. Then, we apply them to Brownian diffusions and solutions to L \'e%DIFDELCMD < }%%% vy driven SDE's under some Lyapunovtype stability assumptions.
 fluency
 0.99901736
 0704.0335
 1

We build a sequence of empirical measures on the space D(R_+,R^d) of R^dvalued c \`a%DIFDELCMD < }%%% dl \`a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^dvalued Markov and Feller process (X_t).
 We build a sequence of empirical measures on the space D(R_+,R^d) of R^dvalued c \`a%DIFDELCMD < }%%% \`a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^dvalued Markov and Feller process (X_t).
 <clarity> <S> We build a sequence of empirical measures on the space D(R_+,R^d) of R^dvalued c \`a%DIFDELCMD < }%%% dl \`a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^dvalued Markov and Feller process (X_t). </S> We obtain some general results of convergence of this sequence. Then, we apply them to Brownian diffusions and solutions to L \'e%DIFDELCMD < }%%% vy driven SDE's under some Lyapunovtype stability assumptions.
 clarity
 0.48871818
 0704.0335
 1

We build a sequence of empirical measures on the space D(R_+,R^d) of R^dvalued c \`a%DIFDELCMD < }%%% dl \`a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^dvalued Markov and Feller process (X_t).
 We build a sequence of empirical measures on the space D(R_+,R^d) of R^dvalued c \`a%DIFDELCMD < }%%% dl %DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^dvalued Markov and Feller process (X_t).
 <fluency> <S> We build a sequence of empirical measures on the space D(R_+,R^d) of R^dvalued c \`a%DIFDELCMD < }%%% dl \`a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^dvalued Markov and Feller process (X_t). </S> We obtain some general results of convergence of this sequence. Then, we apply them to Brownian diffusions and solutions to L \'e%DIFDELCMD < }%%% vy driven SDE's under some Lyapunovtype stability assumptions.
 fluency
 0.9988399
 0704.0335
 1

Then, we apply them to Brownian diffusions and solutions to L \'e%DIFDELCMD < }%%% vy driven SDE's under some Lyapunovtype stability assumptions.
 Then, we apply them to Brownian diffusions and solutions to \'e%DIFDELCMD < }%%% vy driven SDE's under some Lyapunovtype stability assumptions.
 <fluency> We build a sequence of empirical measures on the space D(R_+,R^d) of R^dvalued c \`a%DIFDELCMD < }%%% dl \`a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^dvalued Markov and Feller process (X_t). We obtain some general results of convergence of this sequence. <S> Then, we apply them to Brownian diffusions and solutions to L \'e%DIFDELCMD < }%%% vy driven SDE's under some Lyapunovtype stability assumptions. </S> As a numerical application of this work, we show that this procedure gives an efficient way of option pricing in stochastic volatility models.
 fluency
 0.9979253
 0704.0335
 1

Then, we apply them to Brownian diffusions and solutions to L \'e%DIFDELCMD < }%%% vy driven SDE's under some Lyapunovtype stability assumptions.
 Then, we apply them to Brownian diffusions and solutions to L %DIFDELCMD < }%%% vy driven SDE's under some Lyapunovtype stability assumptions.
 <fluency> We build a sequence of empirical measures on the space D(R_+,R^d) of R^dvalued c \`a%DIFDELCMD < }%%% dl \`a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^dvalued Markov and Feller process (X_t). We obtain some general results of convergence of this sequence. <S> Then, we apply them to Brownian diffusions and solutions to L \'e%DIFDELCMD < }%%% vy driven SDE's under some Lyapunovtype stability assumptions. </S> As a numerical application of this work, we show that this procedure gives an efficient way of option pricing in stochastic volatility models.
 fluency
 0.9034498
 0704.0335
 1

Then, we apply them to Brownian diffusions and solutions to L \'e%DIFDELCMD < }%%% vy driven SDE's under some Lyapunovtype stability assumptions.
 Then, we apply them to Brownian diffusions and solutions to L \'e%DIFDELCMD < }%%% L\'evy driven SDE's under some Lyapunovtype stability assumptions.
 <fluency> We build a sequence of empirical measures on the space D(R_+,R^d) of R^dvalued c \`a%DIFDELCMD < }%%% dl \`a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^dvalued Markov and Feller process (X_t). We obtain some general results of convergence of this sequence. <S> Then, we apply them to Brownian diffusions and solutions to L \'e%DIFDELCMD < }%%% vy driven SDE's under some Lyapunovtype stability assumptions. </S> As a numerical application of this work, we show that this procedure gives an efficient way of option pricing in stochastic volatility models.
 fluency
 0.99883765
 0704.0335
 1

A link between parsimony and consensus trees has already been established by the MRP (matrix representation with parsimony) method of Baum and Ragan \mbox{ Baum1992,Ragan1992 Unless otherwise indicated, the term {\em parsimony} denotes Fitch parsimony.
 Unless otherwise indicated, the term {\em parsimony} denotes Fitch parsimony.
 <coherence> In particular, this paper demonstrates a new mathematical equivalence between Fitch parsimony as well as selection of certain types of consensus trees. The link between parsimony and consensus is intended to contribute to the discussion on parsimony as well as consensus and total evidence. <S> A link between parsimony and consensus trees has already been established by the MRP (matrix representation with parsimony) method of Baum and Ragan \mbox{ Baum1992,Ragan1992 Unless otherwise indicated, the term {\em parsimony} denotes Fitch parsimony. </S>
 coherence
 0.9983072
 0704.0615
 1

Unless otherwise indicated, the term%DIFDELCMD < {\em %%% parsimony denotes Fitch parsimony .
 Unless otherwise indicated, the term%DIFDELCMD < {\em %%% denotes Fitch parsimony .
 <fluency> In particular, this paper demonstrates a new mathematical equivalence between Fitch parsimony as well as selection of certain types of consensus trees. The link between parsimony and consensus is intended to contribute to the discussion on parsimony as well as consensus and total evidence. <S> Unless otherwise indicated, the term%DIFDELCMD < {\em %%% parsimony denotes Fitch parsimony . </S>
 fluency
 0.9981571
 0704.0615
 2

The computational scheme has minimal memory requirements, and is particularly suited for computation on a stream processor, such as a GPU (Graphical Processing Unit).
 The computational scheme has minimal memory requirements, and is also suited for computation on a stream processor, such as a GPU (Graphical Processing Unit).
 <clarity> Several examples taken from neuroscience are given: phototransduction, photopigment bleaching, and spike generation according to the HodgkinHuxley equations. The scheme uses two slightly different forms of autoregressive filters, with an implicit delay of zero for feedforward control and an implicit delay of half a sample distance for feedback control. <S> The computational scheme has minimal memory requirements, and is particularly suited for computation on a stream processor, such as a GPU (Graphical Processing Unit). </S>
 clarity
 0.9981419
 0704.1362
 1

Soft constraints, and related csemiring algebraic structures, prove to be a convenient tool for the management of QoS costs and their compositions along the routes
 Soft constraints, and related csemiring algebraic structures, prove to be a convenient tool for the management of QoS costs and their compositions along the routes .
 <fluency> To attain this, first we translate the network adapting it to a weighted graph (unicast) or andor graph (multicast), where the weight on a connector corresponds to the multidimensional cost of sending a packet on the related network link: each component of the weights vector represents a different QoS metric value (e.g. bandwidth, delay, packet loss). The second step consists in writing this graph as a program in Soft Constraint Logic Programming: the engine of this framework is then able to find the best paths/trees by optimizing their costs and solving the constraints imposed on them (e.g. delay < 40msec), thus finding a solution to QoS routing problem. <S> Soft constraints, and related csemiring algebraic structures, prove to be a convenient tool for the management of QoS costs and their compositions along the routes </S>
 fluency
 0.9992717
 0704.1783
 1

To attain this, first we translate the network adapting it to a weighted graph (unicast) or andor graph (multicast), where the weight on a connector corresponds to the multidimensional cost of sending a packet on the related network link: each component of the weights vector represents a different QoS metric value (e.g. bandwidth, delay, packet loss).
 To attain this, first we translate the network adapting it to a weighted graph (unicast) or andor graph (multicast), where the weight on a connector corresponds to the multidimensional cost of sending a packet on the related network link: each component of the weights vector represents a different QoS metric value (e.g. bandwidth, cost, delay, packet loss).
 <clarity> We present a formal model to represent and solve the unicast/multicast routing problem in networks with Quality of Service (QoS) requirements. <S> To attain this, first we translate the network adapting it to a weighted graph (unicast) or andor graph (multicast), where the weight on a connector corresponds to the multidimensional cost of sending a packet on the related network link: each component of the weights vector represents a different QoS metric value (e.g. bandwidth, delay, packet loss). </S> The second step consists in writing this graph as a program in Soft Constraint Logic Programming : the engine of this framework is then able to find the best paths/trees by optimizing their costs and solving the constraints imposed on them (e.g. delay < 40msec), thus finding a solution to QoS routing problem. Soft constraints, and related csemiring algebraic structures , prove to be a convenient tool for the management of QoS costs and their compositions along the routes .
 clarity
 0.98654246
 0704.1783
 2

Soft constraints, and related csemiring algebraic structures , prove to be a convenient tool for the management of QoS costs and their compositions along the routes .
 Soft constraints, and related csemiring structures are a convenient tool for the management of QoS costs and their compositions along the routes .
 <clarity> To attain this, first we translate the network adapting it to a weighted graph (unicast) or andor graph (multicast), where the weight on a connector corresponds to the multidimensional cost of sending a packet on the related network link: each component of the weights vector represents a different QoS metric value (e.g. bandwidth, delay, packet loss). The second step consists in writing this graph as a program in Soft Constraint Logic Programming : the engine of this framework is then able to find the best paths/trees by optimizing their costs and solving the constraints imposed on them (e.g. delay < 40msec), thus finding a solution to QoS routing problem. <S> Soft constraints, and related csemiring algebraic structures , prove to be a convenient tool for the management of QoS costs and their compositions along the routes . </S>
 clarity
 0.9991903
 0704.1783
 2

At the cellular level, such adjustment relies on the transcription factors which must rapidly find their target sequences amidst a vast amount of nonrelevant sequences on DNA molecules.
 At the cellular level, such adjustment relies on the transcription factors (TFs) which must rapidly find their target sequences amidst a vast amount of nonrelevant sequences on DNA molecules.
 <clarity> Surviving in a diverse environment requires corresponding organism responses. <S> At the cellular level, such adjustment relies on the transcription factors which must rapidly find their target sequences amidst a vast amount of nonrelevant sequences on DNA molecules. </S> Whether these transcription factors locate their target sites through a 1D or 3D pathway is still a matter of speculation. In this paper, we address the latter question using a Monte Carlo simulation by considering a very simple physical model.
 clarity
 0.6861592
 0704.2454
 1

In this paper, we address the latter question using a Monte Carlo simulation by considering a very simple physical model.
 In this paper, we study the above problem using a Monte Carlo simulation by considering a very simple physical model.
 <clarity> At the cellular level, such adjustment relies on the transcription factors which must rapidly find their target sequences amidst a vast amount of nonrelevant sequences on DNA molecules. Whether these transcription factors locate their target sites through a 1D or 3D pathway is still a matter of speculation. <S> In this paper, we address the latter question using a Monte Carlo simulation by considering a very simple physical model. </S> A 1D strip, representing a DNA, with a number of low affinity sites, corresponding to nontarget sites, and high affinity sites, corresponding to target sites, is considered . We examine the 1D and 3D pathways by studying three different particles : a walker that randomly walks along the strip with no dissociation;
 clarity
 0.9975777
 0704.2454
 1

a jumper that dissociates, performs a Brownian motion in space, and then reassociates with the strip at a distant site;
 a jumper that represents dissociation and then reassociation of a TF with the strip at a distant site;
 <clarity> A 1D strip, representing a DNA, with a number of low affinity sites, corresponding to nontarget sites, and high affinity sites, corresponding to target sites, is considered . We examine the 1D and 3D pathways by studying three different particles : a walker that randomly walks along the strip with no dissociation; <S> a jumper that dissociates, performs a Brownian motion in space, and then reassociates with the strip at a distant site; </S> and a hopper that is similar to the jumper but it dissociates and then reassociates at a faster rate than the jumper. We that find jumpers/hoppers reach the equilibrium distribution on a shorter time scale than walkers.
 clarity
 0.99434
 0704.2454
 1

The approach is based on the concept of low order conditional dependence graph that we extend here to Dynamic Bayesian Networks.
 The approach is based on the concept of low order conditional dependence graph that we extend here in the case of Dynamic Bayesian Networks.
 <clarity> In this paper, we propose a novel inference method for dynamic genetic networks which makes it possible to face with a number of time measurements n much smaller than the number of genes p. <S> The approach is based on the concept of low order conditional dependence graph that we extend here to Dynamic Bayesian Networks. </S> Most of our results are based on the theory of graphical models associated with the Directed Acyclic Graphs (DAGs). In this way, we define a minimal DAG G which describes exactly the full order conditional dependencies given the past of the process.
 clarity
 0.97855055
 0704.2551
 2

The inference procedure is implemented in the R package 'G1DBN' freely available from the R archive (CRAN ) .
 The inference procedure is implemented in the R package 'G1DBN' freely available from the CRAN archive .
 <fluency> In general, DAGs G(q) differ from DAG G but still reflect relevant dependence facts for sparse networks such as genetic networks. By using this approximation, we set out a nonbayesian inference method and demonstrate the effectiveness of this approach on both simulated and real data analysis. <S> The inference procedure is implemented in the R package 'G1DBN' freely available from the R archive (CRAN ) . </S>
 fluency
 0.58166283
 0704.2551
 2

This modelling is used to perform a case study on a wellknown pattern recognition benchmark: the UCI Thyroid Disease Database.
 This modeling is used to perform a case study on a wellknown pattern recognition benchmark: the UCI Thyroid Disease Database.
 <fluency> The random initialization of weights of a multilayer perceptron makes it possible to model its training process as a Las Vegas algorithm, i.e. a randomized algorithm which stops when some required training error is obtained, and whose execution time is a random variable. <S> This modelling is used to perform a case study on a wellknown pattern recognition benchmark: the UCI Thyroid Disease Database. </S> Empirical evidence is presented of the training time probability distribution exhibiting a heavy tail behavior, meaning a big probability mass of long executions. This fact is exploited to reduce the training time cost by applying two simple restart strategies.
 fluency
 0.99473876
 0704.2725
 1

This work considers the problem of transmitting multiple compressible sources over a network with minimum cost.
 This work considers the problem of transmitting multiple compressible sources over a network at minimum cost.
 <fluency> <S> This work considers the problem of transmitting multiple compressible sources over a network with minimum cost. </S> The problem is complicated by the fact that the description of the feasible rate region of distributed source coding problems typically has a number of constraints that is exponential in the number of sources that renders general purpose solvers inefficient. We present a framework in which these problems can be solved efficiently by exploiting the structure of the feasible rate regions coupled with dual decomposition and subgradient methods .
 fluency
 0.679199
 0704.2808
 1

The problem is complicated by the fact that the description of the feasible rate region of distributed source coding problems typically has a number of constraints that is exponential in the number of sources that renders general purpose solvers inefficient.
 The problem is complicated by the fact that the description of the feasible rate region of distributed source coding problems typically has a number of constraints that is exponential in the number of sources . This renders general purpose solvers inefficient.
 <coherence> This work considers the problem of transmitting multiple compressible sources over a network with minimum cost. <S> The problem is complicated by the fact that the description of the feasible rate region of distributed source coding problems typically has a number of constraints that is exponential in the number of sources that renders general purpose solvers inefficient. </S> We present a framework in which these problems can be solved efficiently by exploiting the structure of the feasible rate regions coupled with dual decomposition and subgradient methods .
 coherence
 0.998304
 0704.2808
 1

We find that the signal is robust against variations in methods of analysis, but is almost wholly based on fluctuations in the Paleozoic .
 We find that the signal is robust against variations in methods of analysis, and is based on fluctuations in the Paleozoic .
 <clarity> Medvedev and Melott have suggested that periodicity in fossil biodiversity may be induced by cosmic rays which vary as the Solar System oscillates normal to the galactic disk. We reexamine the evidence for a 62 Myr periodicity in biodiversity throughout the Phanerozoic history of animal life reported by Rohde and Muller , as well as related questions of periodicity in origination and extinction. <S> We find that the signal is robust against variations in methods of analysis, but is almost wholly based on fluctuations in the Paleozoic . </S> Examination of origination and extinction is somewhat ambiguous, with results depending upon procedure. Origination and extinction intensity as defined by Rohde and Muller may be affected by an artifact at 27 Myr in the duration of stratigraphic intervals.
 clarity
 0.9469026
 0704.2896
 1

Nevertheless, when a procedure free of this artifact is implemented, the 27 Myr periodicity appears in origination, suggesting that the artifact may be ultimately based upon a signal in the data.
 Nevertheless, when a procedure free of this artifact is implemented, the 27 Myr periodicity appears in origination, suggesting that the artifact may ultimately be based on a signal in the data.
 <fluency> Examination of origination and extinction is somewhat ambiguous, with results depending upon procedure. Origination and extinction intensity as defined by Rohde and Muller may be affected by an artifact at 27 Myr in the duration of stratigraphic intervals. <S> Nevertheless, when a procedure free of this artifact is implemented, the 27 Myr periodicity appears in origination, suggesting that the artifact may be ultimately based upon a signal in the data. </S> A 62 Myr feature appears in extinction, when this same procedure is used. We conclude that evidence for a periodicity at 62 Myr is robust, albeit originating primarily from the Paleozoic part of the dataset while evidence for periodicity at approximately 27 Myr is also present, albeit more ambiguous
 fluency
 0.99924964
 0704.2896
 1

We conclude that evidence for a periodicity at 62 Myr is robust, albeit originating primarily from the Paleozoic part of the dataset while evidence for periodicity at approximately 27 Myr is also present, albeit more ambiguous
 We conclude that evidence for a periodicity at 62 Myr is robust, and evidence for periodicity at approximately 27 Myr is also present, albeit more ambiguous
 <coherence> Nevertheless, when a procedure free of this artifact is implemented, the 27 Myr periodicity appears in origination, suggesting that the artifact may be ultimately based upon a signal in the data. A 62 Myr feature appears in extinction, when this same procedure is used. <S> We conclude that evidence for a periodicity at 62 Myr is robust, albeit originating primarily from the Paleozoic part of the dataset while evidence for periodicity at approximately 27 Myr is also present, albeit more ambiguous </S>
 coherence
 0.9944143
 0704.2896
 1

We conclude that evidence for a periodicity at 62 Myr is robust, albeit originating primarily from the Paleozoic part of the dataset while evidence for periodicity at approximately 27 Myr is also present, albeit more ambiguous
 We conclude that evidence for a periodicity at 62 Myr is robust, albeit originating primarily from the Paleozoic part of the dataset while evidence for periodicity at approximately 27 Myr is also present, albeit more ambiguous .
 <fluency> Nevertheless, when a procedure free of this artifact is implemented, the 27 Myr periodicity appears in origination, suggesting that the artifact may be ultimately based upon a signal in the data. A 62 Myr feature appears in extinction, when this same procedure is used. <S> We conclude that evidence for a periodicity at 62 Myr is robust, albeit originating primarily from the Paleozoic part of the dataset while evidence for periodicity at approximately 27 Myr is also present, albeit more ambiguous </S>
 fluency
 0.9759999
 0704.2896
 1

We provide algorithms for efficiently testing these conditions, and for augmenting a set family in a minimal way to one that satisfies these conditions.
 We also provide algorithms for efficiently testing these conditions, and for augmenting a set family in a minimal way to one that satisfies these conditions.
 <clarity> We give necessary and sufficient conditions on the base of a unionclosed set family that ensures that the family is wellgraded. We consider two cases, depending on whether or not the family contains the empty set. <S> We provide algorithms for efficiently testing these conditions, and for augmenting a set family in a minimal way to one that satisfies these conditions. </S>
 clarity
 0.8929017
 0704.2919
 1

The cellular automata with asynchronous update are used to generate the closetocircular 2dimensional objects revealing the desired features , such as the velocity of the growth and the fractal behavior of their contours.
 We demonstrate the power of the genetic algorithms to construct the cellular automata model simulating the growth of 2dimensional objects revealing the desired features , such as the velocity of the growth and the fractal behavior of their contours.
 <clarity> <S> The cellular automata with asynchronous update are used to generate the closetocircular 2dimensional objects revealing the desired features , such as the velocity of the growth and the fractal behavior of their contours. </S> The approach enables to reproduce and analyze some of the recent findings in morphometric analysis of real tumors with the possible implications for cancer research. The technique is based on cellular automata paradigm with the transition rules searched for by genetic algorithms .
 clarity
 0.9919871
 0704.3138
 1

The cellular automata with asynchronous update are used to generate the closetocircular 2dimensional objects revealing the desired features , such as the velocity of the growth and the fractal behavior of their contours.
 The cellular automata with asynchronous update are used to generate the closetocircular 2dimensional objects revealing the desired properties , such as the velocity of the growth and the fractal behavior of their contours.
 <clarity> <S> The cellular automata with asynchronous update are used to generate the closetocircular 2dimensional objects revealing the desired features , such as the velocity of the growth and the fractal behavior of their contours. </S> The approach enables to reproduce and analyze some of the recent findings in morphometric analysis of real tumors with the possible implications for cancer research. The technique is based on cellular automata paradigm with the transition rules searched for by genetic algorithms .
 clarity
 0.9974591
 0704.3138
 1

The cellular automata with asynchronous update are used to generate the closetocircular 2dimensional objects revealing the desired features , such as the velocity of the growth and the fractal behavior of their contours.
 The cellular automata with asynchronous update are used to generate the closetocircular 2dimensional objects revealing the desired features , such as the growth rate and, at the same time, the fractal behavior of their contours.
 <clarity> <S> The cellular automata with asynchronous update are used to generate the closetocircular 2dimensional objects revealing the desired features , such as the velocity of the growth and the fractal behavior of their contours. </S> The approach enables to reproduce and analyze some of the recent findings in morphometric analysis of real tumors with the possible implications for cancer research. The technique is based on cellular automata paradigm with the transition rules searched for by genetic algorithms .
 clarity
 0.99587137
 0704.3138
 1

During the 2006 FIFA World Cup, we performed an extensive measurement campaign.
 Dur ing the 2006 FIFA World Cup, we performed an extensive measurement campaign.
 <fluency> It is expected that P2P IPTV will contribute to increase the overall Internet traffic. In this context, it is important to measure the impact of P2P IPTV on the networks and to characterize this traffic. <S> During the 2006 FIFA World Cup, we performed an extensive measurement campaign. </S> We measured network traffic generated by broadcasting soccer games by the most popular P2P IPTV applications, namely PPLive, PPStream, SOPCast and TVAnts. From the collected data, we characterized the P2P IPTV traffic structure at different time scales .
 fluency
 0.9991817
 0704.3228
 1

We measured network traffic generated by broadcasting soccer games by the most popular P2P IPTV applications, namely PPLive, PPStream, SOPCast and TVAnts.
 We measured network traffic generated by broadcasting soc cer games by the most popular P2P IPTV applications, namely PPLive, PPStream, SOPCast and TVAnts.
 <fluency> In this context, it is important to measure the impact of P2P IPTV on the networks and to characterize this traffic. During the 2006 FIFA World Cup, we performed an extensive measurement campaign. <S> We measured network traffic generated by broadcasting soccer games by the most popular P2P IPTV applications, namely PPLive, PPStream, SOPCast and TVAnts. </S> From the collected data, we characterized the P2P IPTV traffic structure at different time scales . To the best of our knowledge, this is the first work, which presents a complete multiscale analysis of the P2P IPTV traffic.
 fluency
 0.99829656
 0704.3228
 1

From the collected data, we characterized the P2P IPTV traffic structure at different time scales .
 From the collected data, we charac terized the P2P IPTV traffic structure at different time scales .
 <fluency> During the 2006 FIFA World Cup, we performed an extensive measurement campaign. We measured network traffic generated by broadcasting soccer games by the most popular P2P IPTV applications, namely PPLive, PPStream, SOPCast and TVAnts. <S> From the collected data, we characterized the P2P IPTV traffic structure at different time scales . </S> To the best of our knowledge, this is the first work, which presents a complete multiscale analysis of the P2P IPTV traffic. Our observations show that the network traffic has not the same scale behavior whether the applications use TCP or UDP . For all the applications, the download traffic is different from the upload traffic and the signaling traffic has an impact on the download traffic .
 fluency
 0.98702013
 0704.3228
 1

Our observations show that the network traffic has not the same scale behavior whether the applications use TCP or UDP . For all the applications, the download traffic is different from the upload traffic and the signaling traffic has an impact on the download traffic .
 Our results show that the network traffic has not the same scale behavior whether the applications use TCP or UDP . For all the applications, the download traffic is different from the upload traffic and the signaling traffic has an impact on the download traffic .
 <clarity> From the collected data, we characterized the P2P IPTV traffic structure at different time scales . To the best of our knowledge, this is the first work, which presents a complete multiscale analysis of the P2P IPTV traffic. <S> Our observations show that the network traffic has not the same scale behavior whether the applications use TCP or UDP . For all the applications, the download traffic is different from the upload traffic and the signaling traffic has an impact on the download traffic . </S>
 clarity
 0.99889416
 0704.3228
 1

Our observations show that the network traffic has not the same scale behavior whether the applications use TCP or UDP . For all the applications, the download traffic is different from the upload traffic and the signaling traffic has an impact on the download traffic .
 Our observations show that the network traffic has not the same scale behavior whether the applications use TCP or UDP . For all the applications, the download traffic has different characteristics than the upload traffic and the signaling traffic has an impact on the download traffic .
 <clarity> From the collected data, we characterized the P2P IPTV traffic structure at different time scales . To the best of our knowledge, this is the first work, which presents a complete multiscale analysis of the P2P IPTV traffic. <S> Our observations show that the network traffic has not the same scale behavior whether the applications use TCP or UDP . For all the applications, the download traffic is different from the upload traffic and the signaling traffic has an impact on the download traffic . </S>
 clarity
 0.9984267
 0704.3228
 1

Our observations show that the network traffic has not the same scale behavior whether the applications use TCP or UDP . For all the applications, the download traffic is different from the upload traffic and the signaling traffic has an impact on the download traffic .
 Our observations show that the network traffic has not the same scale behavior whether the applications use TCP or UDP . For all the applications, the download traffic is different from the upload traffic . The signaling traffic has an impact on the download traffic .
 <coherence> From the collected data, we characterized the P2P IPTV traffic structure at different time scales . To the best of our knowledge, this is the first work, which presents a complete multiscale analysis of the P2P IPTV traffic. <S> Our observations show that the network traffic has not the same scale behavior whether the applications use TCP or UDP . For all the applications, the download traffic is different from the upload traffic and the signaling traffic has an impact on the download traffic . </S>
 coherence
 0.99750453
 0704.3228
 1

Our observations show that the network traffic has not the same scale behavior whether the applications use TCP or UDP . For all the applications, the download traffic is different from the upload traffic and the signaling traffic has an impact on the download traffic .
 Our observations show that the network traffic has not the same scale behavior whether the applications use TCP or UDP . For all the applications, the download traffic is different from the upload traffic and the signaling traffic has a significant impact on the download traffic .
 <clarity> From the collected data, we characterized the P2P IPTV traffic structure at different time scales . To the best of our knowledge, this is the first work, which presents a complete multiscale analysis of the P2P IPTV traffic. <S> Our observations show that the network traffic has not the same scale behavior whether the applications use TCP or UDP . For all the applications, the download traffic is different from the upload traffic and the signaling traffic has an impact on the download traffic . </S>
 clarity
 0.9980161
 0704.3228
 1

In the proposed model of computation , the application programming interface, the runtime program, and the computing virtual machine are all represented in the Resource Description Framework (RDF) .
 In the proposed model of computing , the application programming interface, the runtime program, and the computing virtual machine are all represented in the Resource Description Framework (RDF) .
 <fluency> The concepts presented are applicable to any semantic network representation. However, due to the standards and technological infrastructure devoted to the Semantic Web effort, this article is presented from this point of view. <S> In the proposed model of computation , the application programming interface, the runtime program, and the computing virtual machine are all represented in the Resource Description Framework (RDF) . </S> The ramifications of using the same substrate to represent the high and lowlevel aspects of computing are numerous . The implementation of the concepts presented provides a practical computing paradigm that leverages the highlydistributed and standardized representationallayer of the Semantic Web.
 fluency
 0.9608803
 0704.3395
 1

In the proposed model of computation , the application programming interface, the runtime program, and the computing virtual machine are all represented in the Resource Description Framework (RDF) .
 In the proposed model of computation , the application programming interface, the runtime program, and the state of the computing virtual machine are all represented in the Resource Description Framework (RDF) .
 <clarity> The concepts presented are applicable to any semantic network representation. However, due to the standards and technological infrastructure devoted to the Semantic Web effort, this article is presented from this point of view. <S> In the proposed model of computation , the application programming interface, the runtime program, and the computing virtual machine are all represented in the Resource Description Framework (RDF) . </S> The ramifications of using the same substrate to represent the high and lowlevel aspects of computing are numerous . The implementation of the concepts presented provides a practical computing paradigm that leverages the highlydistributed and standardized representationallayer of the Semantic Web.
 clarity
 0.996267
 0704.3395
 1

Using these maps, we prove \pm\pm satisfying 0\le a_{k1}+\lambda a_k+a_{k+1}<1 for some (fixed) \lambda \in \{\pm1\pm\sqrt{5{2},}%DIFDELCMD < \pm%%% \sqrt{2\} } are periodic.
 Using these maps, we prove \pm\pm satisfying 0\le a_{k1}+\lambda a_k+a_{k+1}<1 for some (fixed) \lambda \in \{\pm1\pm\sqrt{5{2},}%DIFDELCMD < \pm%%% \} } are periodic.
 <fluency> We determine periodic and aperiodic points of certain piecewise affine maps in the Euclidean plane. <S> Using these maps, we prove \pm\pm satisfying 0\le a_{k1}+\lambda a_k+a_{k+1}<1 for some (fixed) \lambda \in \{\pm1\pm\sqrt{5{2},}%DIFDELCMD < \pm%%% \sqrt{2\} } are periodic. </S>
 fluency
 0.9872536
 0704.3674
 1

We recently studied the growth of a directed transportation network with a new preferentialattachment scheme , in which a new node attaches to an existing node, i, with a probability inversely proportional to, k, the number of outgoing links at i.
 We study the growth of a directed transportation network with a new preferentialattachment scheme , in which a new node attaches to an existing node, i, with a probability inversely proportional to, k, the number of outgoing links at i.
 <clarity> <S> We recently studied the growth of a directed transportation network with a new preferentialattachment scheme , in which a new node attaches to an existing node, i, with a probability inversely proportional to, k, the number of outgoing links at i. </S> In that model, new nodes make a constant number of links. Therefore, the indegree (or, in foodweb language, prey) distribution is a Kronecker delta function.
 clarity
 0.998741
 0704.3730
 1

It is therefore relevant to the process of gene duplication as a possible cause for the topology of molecular networks.
 It is therefore relevant to the process of gene duplication as a driving force in shaping the topology of molecular networks.
 <clarity> Background: Gene duplication has an essential role in creating new genes in genomes. About 90\% of eucaryotic genes are estimated to be the result of gene duplication. <S> It is therefore relevant to the process of gene duplication as a possible cause for the topology of molecular networks. </S> Results: We extend current models of gene duplication and rewiring by including directions and the fact that molecular networks are not the result of unidirectional growth. We introduce upstream sites and downstream shapes to quantify potential links during duplication and rewiring.
 clarity
 0.9979
 0704.3808
 1

Results: We extend current models of gene duplication and rewiring by including directions and the fact that molecular networks are not the result of unidirectional growth.
 Results: We extend current models of gene duplication and rewiring by including directions and the fact that molecular networks are not a result of unidirectional growth.
 <clarity> About 90\% of eucaryotic genes are estimated to be the result of gene duplication. It is therefore relevant to the process of gene duplication as a possible cause for the topology of molecular networks. <S> Results: We extend current models of gene duplication and rewiring by including directions and the fact that molecular networks are not the result of unidirectional growth. </S> We introduce upstream sites and downstream shapes to quantify potential links during duplication and rewiring. We find that this in itself generate the observed scaling of transcription factors with genome sites in procaryotes.
 clarity
 0.29298508
 0704.3808
 1

We find that this in itself generate the observed scaling of transcription factors with genome sites in procaryotes.
 We find that this in itself generates the observed scaling of transcription factors with genome sites in procaryotes.
 <fluency> Results: We extend current models of gene duplication and rewiring by including directions and the fact that molecular networks are not the result of unidirectional growth. We introduce upstream sites and downstream shapes to quantify potential links during duplication and rewiring. <S> We find that this in itself generate the observed scaling of transcription factors with genome sites in procaryotes. </S> The model can generate a scale free degree distributionwith scaling exponent of 1 n the non growing & case, and with exponent higher than 1 when the network is growing. Conclusions: We find that duplication of genes followed by substantial recombination of upstream regions in principle could generate some main features of genetic regulatory networks.
 fluency
 0.99940705
 0704.3808
 1

We find that this in itself generate the observed scaling of transcription factors with genome sites in procaryotes.
 We find that this in itself generate the observed scaling of transcription factors for genome sites in procaryotes.
 <clarity> Results: We extend current models of gene duplication and rewiring by including directions and the fact that molecular networks are not the result of unidirectional growth. We introduce upstream sites and downstream shapes to quantify potential links during duplication and rewiring. <S> We find that this in itself generate the observed scaling of transcription factors with genome sites in procaryotes. </S> The model can generate a scale free degree distributionwith scaling exponent of 1 n the non growing & case, and with exponent higher than 1 when the network is growing. Conclusions: We find that duplication of genes followed by substantial recombination of upstream regions in principle could generate some main features of genetic regulatory networks.
 clarity
 0.7233195
 0704.3808
 1

The model can generate a scale free degree distributionwith scaling exponent of 1 n the non growing & case, and with exponent higher than 1 when the network is growing.
 The dynamical model can generate a scale free degree distributionwith scaling exponent of 1 n the non growing & case, and with exponent higher than 1 when the network is growing.
 <clarity> We introduce upstream sites and downstream shapes to quantify potential links during duplication and rewiring. We find that this in itself generate the observed scaling of transcription factors with genome sites in procaryotes. <S> The model can generate a scale free degree distributionwith scaling exponent of 1 n the non growing & case, and with exponent higher than 1 when the network is growing. </S> Conclusions: We find that duplication of genes followed by substantial recombination of upstream regions in principle could generate some main features of genetic regulatory networks. We stress that if gene duplication should be a main cause for broad degree distributions, then substantial recombinations between upstream regions of genes are needed to account for the lacking evolutionary relationships between similarly regulated proteins .
 clarity
 0.71853584
 0704.3808
 1

Conclusions: We find that duplication of genes followed by substantial recombination of upstream regions in principle could generate some main features of genetic regulatory networks.
 Conclusions: We find that duplication of genes followed by substantial recombination of upstream regions could generate main features of genetic regulatory networks.
 <clarity> We find that this in itself generate the observed scaling of transcription factors with genome sites in procaryotes. The model can generate a scale free degree distributionwith scaling exponent of 1 n the non growing & case, and with exponent higher than 1 when the network is growing. <S> Conclusions: We find that duplication of genes followed by substantial recombination of upstream regions in principle could generate some main features of genetic regulatory networks. </S> We stress that if gene duplication should be a main cause for broad degree distributions, then substantial recombinations between upstream regions of genes are needed to account for the lacking evolutionary relationships between similarly regulated proteins .
 clarity
 0.9972698
 0704.3808
 1

We stress that if gene duplication should be a main cause for broad degree distributions, then substantial recombinations between upstream regions of genes are needed to account for the lacking evolutionary relationships between similarly regulated proteins .
 We stress that if gene duplication should be a main cause for the observed broad degree distributions, then substantial recombinations between upstream regions of genes are needed to account for the lacking evolutionary relationships between similarly regulated proteins .
 <clarity> The model can generate a scale free degree distributionwith scaling exponent of 1 n the non growing & case, and with exponent higher than 1 when the network is growing. Conclusions: We find that duplication of genes followed by substantial recombination of upstream regions in principle could generate some main features of genetic regulatory networks. <S> We stress that if gene duplication should be a main cause for broad degree distributions, then substantial recombinations between upstream regions of genes are needed to account for the lacking evolutionary relationships between similarly regulated proteins . </S>
 clarity
 0.90747696
 0704.3808
 1

We stress that if gene duplication should be a main cause for broad degree distributions, then substantial recombinations between upstream regions of genes are needed to account for the lacking evolutionary relationships between similarly regulated proteins .
 We stress that if gene duplication should be a main cause for broad degree distributions, then substantial recombinations between upstream regions of genes .
 <clarity> The model can generate a scale free degree distributionwith scaling exponent of 1 n the non growing & case, and with exponent higher than 1 when the network is growing. Conclusions: We find that duplication of genes followed by substantial recombination of upstream regions in principle could generate some main features of genetic regulatory networks. <S> We stress that if gene duplication should be a main cause for broad degree distributions, then substantial recombinations between upstream regions of genes are needed to account for the lacking evolutionary relationships between similarly regulated proteins . </S>
 clarity
 0.9798607
 0704.3808
 1

We show that if m\geq n then \ds %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil%%% \right\rceil \leq \lambda_n(m,k) \leq %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil %%% \right\rceil + C m^2\log k{n} for some constant C.
 We show that if m\geq n then \ds %DIFDELCMD < \lceil%%% {n}}%DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil%%% \right\rceil \leq \lambda_n(m,k) \leq %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil %%% \right\rceil + C m^2\log k{n} for some constant C.
 <clarity> We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D). We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D {is mlabelled} \et \Delta^(D)\leq k\}. <S> We show that if m\geq n then \ds %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil%%% \right\rceil \leq \lambda_n(m,k) \leq %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil %%% \right\rceil + C m^2\log k{n} for some constant C. </S>
 clarity
 0.53114855
 0705.0315
 1

We show that if m\geq n then \ds %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil%%% \right\rceil \leq \lambda_n(m,k) \leq %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil %%% \right\rceil + C m^2\log k{n} for some constant C.
 We show that if m\geq n then \ds %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %DIFDELCMD < %%% {n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil%%% \right\rceil \leq \lambda_n(m,k) \leq %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil %%% \right\rceil + C m^2\log k{n} for some constant C.
 <clarity> We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D). We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D {is mlabelled} \et \Delta^(D)\leq k\}. <S> We show that if m\geq n then \ds %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil%%% \right\rceil \leq \lambda_n(m,k) \leq %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil %%% \right\rceil + C m^2\log k{n} for some constant C. </S>
 clarity
 0.5939261
 0705.0315
 1

We show that if m\geq n then \ds %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil%%% \right\rceil \leq \lambda_n(m,k) \leq %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil %%% \right\rceil + C m^2\log k{n} for some constant C.
 We show that if m\geq n then \ds %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil%%% \right\rceil \leq \lambda_n(m,k) \leq %DIFDELCMD < \lceil%%% {n}}%DIFDELCMD < \lceil %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil %%% \right\rceil + C m^2\log k{n} for some constant C.
 <clarity> We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D). We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D {is mlabelled} \et \Delta^(D)\leq k\}. <S> We show that if m\geq n then \ds %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil%%% \right\rceil \leq \lambda_n(m,k) \leq %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil %%% \right\rceil + C m^2\log k{n} for some constant C. </S>
 clarity
 0.59017307
 0705.0315
 1

We show that if m\geq n then \ds %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil%%% \right\rceil \leq \lambda_n(m,k) \leq %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil %%% \right\rceil + C m^2\log k{n} for some constant C.
 We show that if m\geq n then \ds %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil%%% \right\rceil \leq \lambda_n(m,k) \leq %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %%% {n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil %%% \right\rceil + C m^2\log k{n} for some constant C.
 <clarity> We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D). We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D {is mlabelled} \et \Delta^(D)\leq k\}. <S> We show that if m\geq n then \ds %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil%%% \right\rceil \leq \lambda_n(m,k) \leq %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil %%% \right\rceil + C m^2\log k{n} for some constant C. </S>
 clarity
 0.66324097
 0705.0315
 1

We show that if m\geq n then \ds %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil%%% \right\rceil \leq \lambda_n(m,k) \leq %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil %%% \right\rceil + C m^2\log k{n} for some constant C.
 We show that if m\geq n then \ds %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil%%% \right\rceil \leq \lambda_n(m,k) \leq %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil %%% \right\rceil + C m^2\log k{n} \mbox for some constant C.
 <fluency> We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D). We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D {is mlabelled} \et \Delta^(D)\leq k\}. <S> We show that if m\geq n then \ds %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %DIFDELCMD < %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil%%% \right\rceil \leq \lambda_n(m,k) \leq %DIFDELCMD < \lceil%%% \frac{m{n}}%DIFDELCMD < \lceil %%% \frac{k{n}}%DIFDELCMD < \rceil %%% \left\lceil{n}}\left\lceil {n}}\right\rceil + k{n} %DIFDELCMD < \rceil %%% \right\rceil + C m^2\log k{n} for some constant C. </S>
 fluency
 0.75959563
 0705.0315
 1

A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}.
 A digraph is %DIFDELCMD < {\it %%% mlabelled if every arc is labelled by an integer in \{1, ... \dots ,m\}.
 <fluency> <S> A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}. </S> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring.
 fluency
 0.9994
 0705.0315
 2

A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}.
 A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, \dots ,m\}.
 <fluency> <S> A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}. </S> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring.
 fluency
 0.99616194
 0705.0315
 2

Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 Motivated by wavelength assignment for multicasts in optical networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 <clarity> A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}. <S> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. </S> One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 clarity
 0.99615246
 0705.0315
 2

Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 Motivated by wavelength assignment for multicasts in optical star networks, we %DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 <clarity> A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}. <S> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. </S> One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 clarity
 0.8309773
 0705.0315
 2

Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 <clarity> A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}. <S> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. </S> One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 clarity
 0.99480706
 0705.0315
 2

Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings introduce and study nfibre colourings of labelled digraphs. These are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 <coherence> A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}. <S> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. </S> One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 coherence
 0.99541795
 0705.0315
 2

Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, and for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 <fluency> A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}. <S> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. </S> One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 fluency
 0.9905557
 0705.0315
 2

Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \alpha )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 <clarity> A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}. <S> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. </S> One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 clarity
 0.54657936
 0705.0315
 2

Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \alpha )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 <clarity> A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}. <S> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. </S> One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 clarity
 0.43844983
 0705.0315
 2

Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \alpha ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 <clarity> A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}. <S> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. </S> One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 clarity
 0.5576262
 0705.0315
 2

Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \alpha ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 <clarity> A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}. <S> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. </S> One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 clarity
 0.6776226
 0705.0315
 2

Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda.
 Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there is at least one arc of label l coloured \lambda.
 <clarity> A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}. <S> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. </S> One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 clarity
 0.9985442
 0705.0315
 2

One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring.
 One likes to find the minimum number of colours \lambda_n(D) such that the mlabelled digraph D has an nfiber colouring.
 <fluency> A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}. Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. <S> One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. </S> In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D). We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D).
 fluency
 0.9993382
 0705.0315
 2

One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring.
 One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfibre colouring.
 <fluency> A digraph is %DIFDELCMD < {\it %%% mlabelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}. Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. <S> One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. </S> In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D). We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D).
 fluency
 0.99644804
 0705.0315
 2

In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 In the particular case when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 <fluency> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. <S> In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D). </S> We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D). We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}.
 fluency
 0.99941695
 0705.0315
 2

In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 In the particular case , when D is 1labelled then \lambda_n (D) is %DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 <fluency> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. <S> In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D). </S> We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D). We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}.
 fluency
 0.9987791
 0705.0315
 2

In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% called the directed star arboricity of D, denoted dst(D).
 <clarity> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. <S> In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D). </S> We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D). We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}.
 clarity
 0.99713933
 0705.0315
 2

In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
 In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, and is denoted by dst(D).
 <coherence> Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% nfiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour \lambda , in(v, \lambda )+out(v, \lambda )\leq n with in(v, \lambda ) the number of arcs coloured \lambda entering v and out(v, \lambda ) the number of labels l such that there exists an arc leaving v of label l coloured \lambda. One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. <S> In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D). </S> We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D). We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}.
 coherence
 0.99799937
 0705.0315
 2

We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D).
 We first show that dst(D)\leq 2\Delta^(D)+1 , and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D).
 <fluency> One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D). <S> We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D). </S> We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}. We show that if m\geq n then \ds \left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil\leq \lambda_n(m,k) \leq\left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil + C \frac{m^2\log k}{n} \mbox for some constant C. %DIFDELCMD < }%%%
 fluency
 0.9958171
 0705.0315
 2

We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D).
 We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 , then dst(D)\leq 2\Delta^(D).
 <fluency> One likes to find the minimum number of colours \lambda_n(D) such that an mlabbelled digraph D has an nfiber colouring. In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D). <S> We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D). </S> We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}. We show that if m\geq n then \ds \left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil\leq \lambda_n(m,k) \leq\left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil + C \frac{m^2\log k}{n} \mbox for some constant C. %DIFDELCMD < }%%%
 fluency
 0.9968265
 0705.0315
 2

We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}.
 We also prove that for a subcubic digraph D, then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}.
 <clarity> In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D). We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D). <S> We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}. </S> We show that if m\geq n then \ds \left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil\leq \lambda_n(m,k) \leq\left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil + C \frac{m^2\log k}{n} \mbox for some constant C. %DIFDELCMD < }%%%
 clarity
 0.9816679
 0705.0315
 2

We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}.
 We also prove that if D is subcubic then dst(D)\leq 3 , and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}.
 <fluency> In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D). We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D). <S> We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}. </S> We show that if m\geq n then \ds \left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil\leq \lambda_n(m,k) \leq\left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil + C \frac{m^2\log k}{n} \mbox for some constant C. %DIFDELCMD < }%%%
 fluency
 0.9986375
 0705.0315
 2

We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}.
 We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 , then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}.
 <fluency> In the particular case , when D is 1labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D). We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D). <S> We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}. </S> We show that if m\geq n then \ds \left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil\leq \lambda_n(m,k) \leq\left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil + C \frac{m^2\log k}{n} \mbox for some constant C. %DIFDELCMD < }%%%
 fluency
 0.9985385
 0705.0315
 2

We show that if m\geq n then \ds \left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil\leq \lambda_n(m,k) \leq\left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil + C \frac{m^2\log k}{n} \mbox for some constant C. %DIFDELCMD < }%%%
 We show that if m\geq n , then \ds \left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil\leq \lambda_n(m,k) \leq\left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil + C \frac{m^2\log k}{n} \mbox for some constant C. %DIFDELCMD < }%%%
 <fluency> We first show that dst(D)\leq 2\Delta^(D)+1 and conjecture that if \Delta^(D)\geq 2 then dst(D)\leq 2\Delta^(D). We also prove that if D is subcubic then dst(D)\leq 3 and that if \Delta^+(D), \Delta^(D)\leq 2 then dst(D)\leq 4. Finally, we study \lambda_n(m,k)=\max\{\lambda_n(D) \tq D %DIFDELCMD < {%%% is mlabelled \et \Delta^(D)\leq k\}. <S> We show that if m\geq n then \ds \left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil\leq \lambda_n(m,k) \leq\left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil + C \frac{m^2\log k}{n} \mbox for some constant C. %DIFDELCMD < }%%% </S>
 fluency
 0.97875667
 0705.0315
 2

For block size B and cache size M , the mesh update cost is O(1+G =B) , assuming the tall cache assumption M= \Omega (B^d) , where d is the dimensionality of the mesh 's geometric domain.
 For block size B , and cache size M , the mesh update cost is O(1+G =B) , assuming the tall cache assumption M= \Omega (B^d) , where d is the dimensionality of the mesh 's geometric domain.
 <clarity> This paper shows how to generate a cacheoblivious memory layout of a wellshaped finiteelement mesh G. This cacheoblivious mesh layout enables asymptotically optimal mesh updates, in which each vertex communicates with all of its neighbors. Mesh updates is the building block of iterative linear system solver. <S> For block size B and cache size M , the mesh update cost is O(1+G =B) , assuming the tall cache assumption M= \Omega (B^d) , where d is the dimensionality of the mesh 's geometric domain. </S> The layout algorithm runs cacheobliviously in O(G log ^2G) operations and O(1+G (log^2 G )/B) memory transfers with high probability. The approach combines ideas from VLSI theory, graph separators, and I/Oefficient computing, and presents simplified and improved methods for building fullybalanced decomposition trees from the VLSI literature and kway partitioning from the graphseparator literature.
 clarity
 0.9165182
 0705.1033
 1

For block size B and cache size M , the mesh update cost is O(1+G =B) , assuming the tall cache assumption M= \Omega (B^d) , where d is the dimensionality of the mesh 's geometric domain.
 For block size B and cache size M , the mesh update cost is O(1+G =B) , assuming the tall cache assumption M= o (B^d) , where d is the dimensionality of the mesh 's geometric domain.
 <clarity> This paper shows how to generate a cacheoblivious memory layout of a wellshaped finiteelement mesh G. This cacheoblivious mesh layout enables asymptotically optimal mesh updates, in which each vertex communicates with all of its neighbors. Mesh updates is the building block of iterative linear system solver. <S> For block size B and cache size M , the mesh update cost is O(1+G =B) , assuming the tall cache assumption M= \Omega (B^d) , where d is the dimensionality of the mesh 's geometric domain. </S> The layout algorithm runs cacheobliviously in O(G log ^2G) operations and O(1+G (log^2 G )/B) memory transfers with high probability. The approach combines ideas from VLSI theory, graph separators, and I/Oefficient computing, and presents simplified and improved methods for building fullybalanced decomposition trees from the VLSI literature and kway partitioning from the graphseparator literature.
 clarity
 0.6148963
 0705.1033
 1

We then introduce the relaxedbalanced decomposition tree and show that with M = \Omega(B^d), mesh update cost is O(1+ G/B) . We give a layout algorithm for relaxedbalanced decomposition trees, which runs cacheobliviously in O( G log G loglog G )operations and O(1+G  log G log log G) memory transfers with high probability .
 We then introduce the relaxedbalanced decomposition tree and show that with M = \Omega(B^d), mesh update cost is O(1+ ( G/B) . We give a layout algorithm for relaxedbalanced decomposition trees, which runs cacheobliviously in O( G log G loglog G )operations and O(1+G  log G log log G) memory transfers with high probability .
 <fluency> The layout algorithm runs cacheobliviously in O(G log ^2G) operations and O(1+G (log^2 G )/B) memory transfers with high probability. The approach combines ideas from VLSI theory, graph separators, and I/Oefficient computing, and presents simplified and improved methods for building fullybalanced decomposition trees from the VLSI literature and kway partitioning from the graphseparator literature. <S> We then introduce the relaxedbalanced decomposition tree and show that with M = \Omega(B^d), mesh update cost is O(1+ G/B) . We give a layout algorithm for relaxedbalanced decomposition trees, which runs cacheobliviously in O( G log G loglog G )operations and O(1+G  log G log log G) memory transfers with high probability . </S>
 fluency
 0.99897313
 0705.1033
 1

We then introduce the relaxedbalanced decomposition tree and show that with M = \Omega(B^d), mesh update cost is O(1+ G/B) . We give a layout algorithm for relaxedbalanced decomposition trees, which runs cacheobliviously in O( G log G loglog G )operations and O(1+G  log G log log G) memory transfers with high probability .
 We then introduce the relaxedbalanced decomposition tree and show that with M = \Omega(B^d), mesh update cost is O(1+ G/B) . We give a layout algorithm for relaxedbalanced decomposition trees, which runs cacheobliviously in O( G log G loglog G  log G log log G) memory transfers with high probability .
 <clarity> The layout algorithm runs cacheobliviously in O(G log ^2G) operations and O(1+G (log^2 G )/B) memory transfers with high probability. The approach combines ideas from VLSI theory, graph separators, and I/Oefficient computing, and presents simplified and improved methods for building fullybalanced decomposition trees from the VLSI literature and kway partitioning from the graphseparator literature. <S> We then introduce the relaxedbalanced decomposition tree and show that with M = \Omega(B^d), mesh update cost is O(1+ G/B) . We give a layout algorithm for relaxedbalanced decomposition trees, which runs cacheobliviously in O( G log G loglog G )operations and O(1+G  log G log log G) memory transfers with high probability . </S>
 clarity
 0.9380132
 0705.1033
 1

Hayashi and Carthew (Nature 431 [2004], 647) have shown that the packing of cone cells in the Drosophila retina resembles soap bubble packing, and that changing cadherin expression can change this packing and cell shape.
 Hayashi and Carthew (Nature 431 [2004], 647) have shown that the packing of cone cells in the Drosophila retina resembles soap bubble packing, and that changing cadherin expression can change this packing , as well as cell shape.
 <clarity> <S> Hayashi and Carthew (Nature 431 [2004], 647) have shown that the packing of cone cells in the Drosophila retina resembles soap bubble packing, and that changing cadherin expression can change this packing and cell shape. </S> We here ask which surface mechanics are involved in the establishment of cell topology and geometry. We model, using a minimal set of parameters based upon experimental observations, the topology and geometry of wildtype cone cells, as well as mutants with different amounts of cellsor changed expression of cadherin molecules.
 clarity
 0.9887189
 0705.1057
 1

The efficiencies of the mechanisms and the nature of the induced, timedependent flow fields are found to differ widely among swimmers .
 The swimming efficiency and the nature of the induced, timedependent flow fields are found to differ widely among swimmers .
 <clarity> The advantage of the atomistic approach is that the detailed level of description allows complete freedom in specifying the swimmer design and its coupling with the surrounding fluid. A series of twodimensional swimming bodies employing a variety of propulsion mechanisms  motivated by biological and microrobotic designs  is investigated, including the use of moving limbs, changing body shapes and fluid jets. <S> The efficiencies of the mechanisms and the nature of the induced, timedependent flow fields are found to differ widely among swimmers . </S>
 clarity
 0.9982516
 0705.1606
 1

The efficiencies of the mechanisms and the nature of the induced, timedependent flow fields are found to differ widely among swimmers .
 The efficiencies of the mechanisms and the nature of the induced, timedependent flow fields are found to differ widely among body designs and propulsion mechanisms .
 <clarity> The advantage of the atomistic approach is that the detailed level of description allows complete freedom in specifying the swimmer design and its coupling with the surrounding fluid. A series of twodimensional swimming bodies employing a variety of propulsion mechanisms  motivated by biological and microrobotic designs  is investigated, including the use of moving limbs, changing body shapes and fluid jets. <S> The efficiencies of the mechanisms and the nature of the induced, timedependent flow fields are found to differ widely among swimmers . </S>
 clarity
 0.73531395
 0705.1606
 1

Similaritymeasure based clustering is a crucial problem appearing throughout scientific data analysis.
 Motivation: Similaritymeasure based clustering is a crucial problem appearing throughout scientific data analysis.
 <coherence> <S> Similaritymeasure based clustering is a crucial problem appearing throughout scientific data analysis. </S> Recently, a powerful new algorithm called Affinity Propagation (AP) based on messagepassing techniques was proposed by Frey and Dueck . In AP, each cluster is identified by a common exemplar all other data points of the same cluster refer to . Since the exemplars in AP are itselves data points, they have to refer to themselves.
 coherence
 0.6425086
 0705.2646
 1

In AP, each cluster is identified by a common exemplar all other data points of the same cluster refer to . Since the exemplars in AP are itselves data points, they have to refer to themselves.
 In AP, each cluster is identified by a common exemplar all other data points of the same cluster refer to , and exemplars have to refer to themselves.
 <coherence> Similaritymeasure based clustering is a crucial problem appearing throughout scientific data analysis. Recently, a powerful new algorithm called Affinity Propagation (AP) based on messagepassing techniques was proposed by Frey and Dueck . <S> In AP, each cluster is identified by a common exemplar all other data points of the same cluster refer to . Since the exemplars in AP are itselves data points, they have to refer to themselves. </S> Albeit its proved power, AP in its present form suffers from a number of drawbacks. The hard constraint of having exactly one exemplar in each cluster restricts the applicability of AP to classes of regularly shaped clusters, and leads to suboptimal performance, {\it e.g. , in analyzing gene expression data.
 coherence
 0.99798703
 0705.2646
 1

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Paper: Read, Revise, Repeat: A System Demonstration for Humanintheloop Iterative Text Revision
Authors: Wanyu Du*, Zae Myung Kim*, Vipul Raheja, Dhruv Kumar, Dongyeop Kang
Github repo: https://github.com/vipulraheja/IteraTeR
Watch our system demonstration below!