# Datasets: wanyu /IteraTeR_v2

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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 Michaelis-Menten quasi-steady state conditions, there are at most n+1 steady states; and (4) for parameters far from the standard Michaelis-Menten quasi-steady 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 non-isomorphism 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 non-isomorphism 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 non-isomorphism 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 non-isomorphism 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 non-isomorphism 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 non-isomorphism 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 non-isomorphism 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^d-valued c \a%DIFDELCMD < }%%% dl \a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^d-valued Markov and Feller process (X_t).
We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued \a%DIFDELCMD < }%%% dl \a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^d-valued Markov and Feller process (X_t).
<clarity> <S> We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c \a%DIFDELCMD < }%%% dl \a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^d-valued 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 Lyapunov-type stability assumptions.
clarity
0.9913898
0704.0335
1
We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c \a%DIFDELCMD < }%%% dl \a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^d-valued Markov and Feller process (X_t).
We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c %DIFDELCMD < }%%% dl \a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^d-valued Markov and Feller process (X_t).
<fluency> <S> We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c \a%DIFDELCMD < }%%% dl \a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^d-valued 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 Lyapunov-type stability assumptions.
fluency
0.99901736
0704.0335
1
We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c \a%DIFDELCMD < }%%% dl \a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^d-valued Markov and Feller process (X_t).
We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c \a%DIFDELCMD < }%%% \a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^d-valued Markov and Feller process (X_t).
<clarity> <S> We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c \a%DIFDELCMD < }%%% dl \a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^d-valued 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 Lyapunov-type stability assumptions.
clarity
0.48871818
0704.0335
1
We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c \a%DIFDELCMD < }%%% dl \a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^d-valued Markov and Feller process (X_t).
We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c \a%DIFDELCMD < }%%% dl %DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^d-valued Markov and Feller process (X_t).
<fluency> <S> We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c \a%DIFDELCMD < }%%% dl \a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^d-valued 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 Lyapunov-type 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 Lyapunov-type stability assumptions.
Then, we apply them to Brownian diffusions and solutions to \'e%DIFDELCMD < }%%% vy driven SDE's under some Lyapunov-type stability assumptions.
<fluency> We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c \a%DIFDELCMD < }%%% dl \a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^d-valued 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 Lyapunov-type 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 Lyapunov-type stability assumptions.
Then, we apply them to Brownian diffusions and solutions to L %DIFDELCMD < }%%% vy driven SDE's under some Lyapunov-type stability assumptions.
<fluency> We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c \a%DIFDELCMD < }%%% dl \a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^d-valued 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 Lyapunov-type 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 Lyapunov-type stability assumptions.
Then, we apply them to Brownian diffusions and solutions to L \'e%DIFDELCMD < }%%% L\'evy driven SDE's under some Lyapunov-type stability assumptions.
<fluency> We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c \a%DIFDELCMD < }%%% dl \a%DIFDELCMD < }%%% g functions on R_+ in order to approximate the law of a stationary R^d-valued 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 Lyapunov-type 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 Hodgkin-Huxley 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 c-semiring algebraic structures, prove to be a convenient tool for the management of QoS costs and their compositions along the routes
Soft constraints, and related c-semiring 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 and-or 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 c-semiring 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 and-or 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 and-or 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 and-or 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 c-semiring 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 c-semiring algebraic structures , prove to be a convenient tool for the management of QoS costs and their compositions along the routes .
Soft constraints, and related c-semiring 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 and-or 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 c-semiring 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 non-relevant 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 non-relevant 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 non-relevant 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 non-relevant 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 non-target 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 re-associates with the strip at a distant site;
a jumper that represents dissociation and then re-association 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 non-target 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 re-associates with the strip at a distant site; </S> and a hopper that is similar to the jumper but it dissociates and then re-associates 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 non-bayesian 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 well-known pattern recognition benchmark: the UCI Thyroid Disease Database.
This modeling is used to perform a case study on a well-known 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 well-known 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 re-examine 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 union-closed set family that ensures that the family is well-graded. 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 close-to-circular 2-dimensional 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 2-dimensional 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 close-to-circular 2-dimensional 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 close-to-circular 2-dimensional 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 close-to-circular 2-dimensional 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 close-to-circular 2-dimensional 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 close-to-circular 2-dimensional 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 close-to-circular 2-dimensional 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 close-to-circular 2-dimensional 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 run-time 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 run-time 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 run-time 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 low-level aspects of computing are numerous . The implementation of the concepts presented provides a practical computing paradigm that leverages the highly-distributed and standardized representational-layer of the Semantic Web.
fluency
0.9608803
0704.3395
1
In the proposed model of computation , the application programming interface, the run-time 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 run-time 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 run-time 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 low-level aspects of computing are numerous . The implementation of the concepts presented provides a practical computing paradigm that leverages the highly-distributed and standardized representational-layer of the Semantic Web.
clarity
0.996267
0704.3395
1
Using these maps, we prove \pm\pm satisfying 0\le a_{k-1}+\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_{k-1}+\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_{k-1}+\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 preferential-attachment 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 preferential-attachment 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 preferential-attachment 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 food-web 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 m-labelled} \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 m-labelled} \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 m-labelled} \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 m-labelled} \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 m-labelled} \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 %%% m-labelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}.
A digraph is %DIFDELCMD < {\it %%% m-labelled if every arc is labelled by an integer in \{1, ... \dots ,m\}.
<fluency> <S> A digraph is %DIFDELCMD < {\it %%% m-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring.
fluency
0.9994
0705.0315
2
A digraph is %DIFDELCMD < {\it %%% m-labelled if every arcs is labelled by an integer in \{1, ... \dots ,m\}.
A digraph is %DIFDELCMD < {\it %%% m-labelled if every arcs is labelled by an integer in \{1, \dots ,m\}.
<fluency> <S> A digraph is %DIFDELCMD < {\it %%% m-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring.
fluency
0.99616194
0705.0315
2
Motivated by wavelength assignment for multicasts in optical star networks, we study%DIFDELCMD < {\it %%% n-fiber 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 %%% n-fiber 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 %%% m-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. In the particular case , when D is 1-labelled 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 %%% n-fiber 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 %%% n-fiber 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 %%% m-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. In the particular case , when D is 1-labelled 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 %%% n-fiber 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 %%% m-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. In the particular case , when D is 1-labelled 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 %%% n-fiber 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 %%% n-fiber colourings introduce and study n-fibre 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 %%% m-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. In the particular case , when D is 1-labelled 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 %%% n-fiber 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 %%% n-fiber 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 %%% m-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. In the particular case , when D is 1-labelled 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 %%% n-fiber 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 %%% n-fiber 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 %%% m-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. In the particular case , when D is 1-labelled 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 %%% n-fiber 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 %%% n-fiber 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 %%% m-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. In the particular case , when D is 1-labelled 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 %%% n-fiber 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 %%% n-fiber 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 %%% m-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. In the particular case , when D is 1-labelled 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 %%% n-fiber 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 %%% n-fiber 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 %%% m-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. In the particular case , when D is 1-labelled 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 %%% n-fiber 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 %%% n-fiber 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 %%% m-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. In the particular case , when D is 1-labelled 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 m-labbelled digraph D has an n-fiber colouring.
One likes to find the minimum number of colours \lambda_n(D) such that the m-labelled digraph D has an n-fiber colouring.
<fluency> A digraph is %DIFDELCMD < {\it %%% m-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. </S> In the particular case , when D is 1-labelled 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 m-labbelled digraph D has an n-fiber colouring.
One likes to find the minimum number of colours \lambda_n(D) such that an m-labbelled digraph D has an n-fibre colouring.
<fluency> A digraph is %DIFDELCMD < {\it %%% m-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. </S> In the particular case , when D is 1-labelled 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 1-labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
In the particular case when D is 1-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. <S> In the particular case , when D is 1-labelled 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 m-labelled \et \Delta^-(D)\leq k\}.
fluency
0.99941695
0705.0315
2
In the particular case , when D is 1-labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
In the particular case , when D is 1-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. <S> In the particular case , when D is 1-labelled 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 m-labelled \et \Delta^-(D)\leq k\}.
fluency
0.9987791
0705.0315
2
In the particular case , when D is 1-labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
In the particular case , when D is 1-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. <S> In the particular case , when D is 1-labelled 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 m-labelled \et \Delta^-(D)\leq k\}.
clarity
0.99713933
0705.0315
2
In the particular case , when D is 1-labelled then \lambda_n (D) is the%DIFDELCMD < {\it %%% directed star arboricty of D, denoted dst(D).
In the particular case , when D is 1-labelled 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 %%% n-fiber 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 m-labbelled digraph D has an n-fiber colouring. <S> In the particular case , when D is 1-labelled 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 m-labelled \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 m-labbelled digraph D has an n-fiber colouring. In the particular case , when D is 1-labelled 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 m-labelled \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 m-labbelled digraph D has an n-fiber colouring. In the particular case , when D is 1-labelled 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 m-labelled \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 m-labelled \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 m-labelled \et \Delta^-(D)\leq k\}.
<clarity> In the particular case , when D is 1-labelled 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 m-labelled \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 m-labelled \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 m-labelled \et \Delta^-(D)\leq k\}.
<fluency> In the particular case , when D is 1-labelled 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 m-labelled \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 m-labelled \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 m-labelled \et \Delta^-(D)\leq k\}.
<fluency> In the particular case , when D is 1-labelled 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 m-labelled \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 m-labelled \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 cache-oblivious memory layout of a well-shaped finite-element mesh G. This cache-oblivious 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 cache-obliviously in O(|G| log ^2|G|) 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/O-efficient computing, and presents simplified and improved methods for building fully-balanced decomposition trees from the VLSI literature and k-way partitioning from the graph-separator 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 cache-oblivious memory layout of a well-shaped finite-element mesh G. This cache-oblivious 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 cache-obliviously in O(|G| log ^2|G|) 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/O-efficient computing, and presents simplified and improved methods for building fully-balanced decomposition trees from the VLSI literature and k-way partitioning from the graph-separator literature.
clarity
0.6148963
0705.1033
1
We then introduce the relaxed-balanced decomposition tree and show that with M = \Omega(B^d), mesh update cost is O(1+ |G|/B) . We give a layout algorithm for relaxed-balanced decomposition trees, which runs cache-obliviously 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 relaxed-balanced decomposition tree and show that with M = \Omega(B^d), mesh update cost is O(1+ ( |G|/B) . We give a layout algorithm for relaxed-balanced decomposition trees, which runs cache-obliviously 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 cache-obliviously in O(|G| log ^2|G|) 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/O-efficient computing, and presents simplified and improved methods for building fully-balanced decomposition trees from the VLSI literature and k-way partitioning from the graph-separator literature. <S> We then introduce the relaxed-balanced decomposition tree and show that with M = \Omega(B^d), mesh update cost is O(1+ |G|/B) . We give a layout algorithm for relaxed-balanced decomposition trees, which runs cache-obliviously 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 relaxed-balanced decomposition tree and show that with M = \Omega(B^d), mesh update cost is O(1+ |G|/B) . We give a layout algorithm for relaxed-balanced decomposition trees, which runs cache-obliviously 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 relaxed-balanced decomposition tree and show that with M = \Omega(B^d), mesh update cost is O(1+ |G|/B) . We give a layout algorithm for relaxed-balanced decomposition trees, which runs cache-obliviously in O( |G| log |G| loglog |G | log |G| log log |G|) memory transfers with high probability .
<clarity> The layout algorithm runs cache-obliviously in O(|G| log ^2|G|) 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/O-efficient computing, and presents simplified and improved methods for building fully-balanced decomposition trees from the VLSI literature and k-way partitioning from the graph-separator literature. <S> We then introduce the relaxed-balanced decomposition tree and show that with M = \Omega(B^d), mesh update cost is O(1+ |G|/B) . We give a layout algorithm for relaxed-balanced decomposition trees, which runs cache-obliviously 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, time-dependent flow fields are found to differ widely among swimmers .
The swimming efficiency and the nature of the induced, time-dependent 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 two-dimensional 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, time-dependent 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, time-dependent flow fields are found to differ widely among swimmers .
The efficiencies of the mechanisms and the nature of the induced, time-dependent 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 two-dimensional 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, time-dependent flow fields are found to differ widely among swimmers . </S>
clarity
0.73531395
0705.1606
1
Similarity-measure based clustering is a crucial problem appearing throughout scientific data analysis.
Motivation: Similarity-measure based clustering is a crucial problem appearing throughout scientific data analysis.
<coherence> <S> Similarity-measure based clustering is a crucial problem appearing throughout scientific data analysis. </S> Recently, a powerful new algorithm called Affinity Propagation (AP) based on message-passing 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> Similarity-measure based clustering is a crucial problem appearing throughout scientific data analysis. Recently, a powerful new algorithm called Affinity Propagation (AP) based on message-passing 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
End of preview (truncated to 100 rows)
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Authors: Wanyu Du*, Zae Myung Kim*, Vipul Raheja, Dhruv Kumar, Dongyeop Kang

Github repo: https://github.com/vipulraheja/IteraTeR

Watch our system demonstration below!