wanyu/IteraTeR_v2 huggingface dataset:
Original: In this work we study the asymptotic traffic behavior for Gromov's hyperbolic networks as the size of the network increases .
Revised: In this work we study the asymptotic traffic behavior for Gromov's hyperbolic graphs .
Edit intent: clarity
Original:  We prove that under certain mild hypothesis the traffic in a large hyperbolic network tends to pass through a finite set of highly congested nodes.
Revised:  We prove that under certain mild hypotheses the traffic flow in a hyperbolic graph tends to pass through a finite set of highly congested nodes.
Edit intent: clarity
Original:  These nodes will be called the `` core" of the network .
Revised:  These nodes are called the " core" of the network .
Edit intent: clarity
Original:  These nodes will be called the `` core" of the network .
Revised:  These nodes will be called the `` core" of the graph .
Edit intent: clarity
Original:  We provide a formal definition of the core in a very general context and we study the properties of this set for hyperbolic graphs.
Revised:  We provide a formal definition of the core in a very general context and we study the properties of this set for several graphs.
Edit intent: clarity
Original: In this work we study the asymptotic traffic behavior in Gromov's hyperbolic spaces when the traffic decays exponentially with the distance.
Revised: In this work we study the asymptotic traffic flow in Gromov's hyperbolic spaces when the traffic decays exponentially with the distance.
Edit intent: clarity
Original: In this work we study the asymptotic traffic behavior in Gromov's hyperbolic spaces when the traffic decays exponentially with the distance.
Revised: In this work we study the asymptotic traffic behavior in Gromov's hyperbolic graphs when the traffic decays exponentially with the distance.
Edit intent: clarity
Original:  We prove that under general conditions, there exist a phase transition between local and global traffic.
Revised:  We prove that under general conditions, there exists a phase transition between local and global traffic.
Edit intent: fluency
Original:  More specifically, assume that the traffic rate between two nodes u and v is given by R(u,v)=\beta^{-d(u,v)} where d(u,v) is the distance between the nodes , then there exists a constant D that depends on the geometry of the network such that if 1< \beta<D the traffic is global and there is a small set of highly congested nodes called the core.
Revised:  More specifically, assume that the traffic rate between two nodes u and v is given by R(u,v)=\beta^{-d(u,v)} where d(u,v) is the distance between the nodes . Then there exists a constant D that depends on the geometry of the network such that if 1< \beta<D the traffic is global and there is a small set of highly congested nodes called the core.
Edit intent: fluency
Original: The study of a two-species dynamics population model, which includes intraspecific competition to the Lotka-Volterra equation, is presented . Despite being simple  , this model presents a very rich behavior , spanning on several ecological regimes.
Revised: The two-species dynamics population model, which includes intraspecific competition to the Lotka-Volterra equation, is presented . Despite being simple , this model presents a very rich behavior , spanning on several ecological regimes.
Edit intent: clarity
Original:  From the stability of the steady state solutions, two phases are obtained ,namely extinction of one species or their coexistence .
Revised:  From the stability of the steady state solutions, two phases are obtained : (i) extinction of one species or their coexistence .
Edit intent: clarity
Original:  We give an algorithm that attains an approximation ratio of O( log n loglog Delta ), where n is the number of links and Delta is the ratio between the longest and the shortest linklength . Under the natural assumption that lengths are represented in binary, this gives the first polylog(n)-approximation .
Revised:  We give an algorithm that attains an approximation ratio of O( log n loglog Delta ), where n is the number of links and Delta is the ratio between the longest and the shortest link length . Under the natural assumption that lengths are represented in binary, this gives the first polylog(n)-approximation .
Edit intent: fluency
Original:  We also give a simple online algorithm that yields a O(log Delta)-approximation, by a reduction to the coloring of unit-disc graphs.
Edit intent: coherence
Original:  The constitutive relations for a mixture of a viscoelastic solid and a fluid (specifically Newtonian fluid) are derived using ideas from the classical theory of mixtures and a thermodynamic framework based on the notion of maximization of the rate of entropy production .
Revised:  Using ideas from the classical theory of mixtures and a thermodynamic framework based on the notion of maximization of the rate of entropy production .
Edit intent: coherence
Original:  We prescribe forms for the specific Helmholtz potential and the rate of dissipation and the relations for the partial stress in the solid, the partial stress in the fluid, and the interaction force between the solid and the fluid, and the evolution equation of the natural configuration of the solid are derived .
Revised:  We prescribe forms for the specific Helmholtz potential and the rate of dissipation , we derive the relations for the partial stress in the solid, the partial stress in the fluid, and the interaction force between the solid and the fluid, and the evolution equation of the natural configuration of the solid are derived .
Edit intent: coherence
Original:  We prescribe forms for the specific Helmholtz potential and the rate of dissipation and the relations for the partial stress in the solid, the partial stress in the fluid, and the interaction force between the solid and the fluid, and the evolution equation of the natural configuration of the solid are derived .
Revised:  We prescribe forms for the specific Helmholtz potential and the rate of dissipation and the relations for the partial stress in the solid, the partial stress in the fluid, the interaction force between the solid and the fluid, and the evolution equation of the natural configuration of the solid are derived .
Edit intent: fluency
Original:  We prescribe forms for the specific Helmholtz potential and the rate of dissipation and the relations for the partial stress in the solid, the partial stress in the fluid, and the interaction force between the solid and the fluid, and the evolution equation of the natural configuration of the solid are derived .
Revised:  We prescribe forms for the specific Helmholtz potential and the rate of dissipation and the relations for the partial stress in the solid, the partial stress in the fluid, and the interaction force between the solid and the fluid, and the evolution equation of the natural configuration of the solid .
Edit intent: clarity
Original:  We also study the swelling of a viscoelastic solid under the application of an external force  .
Revised:  The swelling of a viscoelastic solid under the application of an external force .
Edit intent: clarity
Original:  When the local dynamical stability of the network is plotted as a function of the two delays  a pattern of tongues is revealed.
Revised:  When the local dynamical stability of the network is plotted as a function of the two delays then a pattern of tongues is revealed.
Edit intent: coherence
Original: The (bounded) hairpin completion and its iterated versions are operations on formal languages which have been inspired by the hairpin formation in DNA-biochemistry.
Revised: The (bounded) hairpin completion and its iterated versions are operations on formal lan- guages which have been inspired by the hairpin formation in DNA-biochemistry.
Edit intent: fluency
Original:  Here we show that this is true by providing actually more general result which applies to all  classes of languages provided they fulfill some basic closure properties.
Revised:  Here we show that this is true by providing actually more general result which applies to all the classes of languages provided they fulfill some basic closure properties.
Edit intent: fluency
Original:  Here we exhibit an example of a singleton where the iterated hairpin completion leads to a language which is not context-free  .
Revised:  Here we exhibit an example of a singleton language whose iterated hairpin completion leads to a language which is not context-free .
Edit intent: clarity
Original:  Here we exhibit an example of a singleton where the iterated hairpin completion leads to a language which is not context-free  .
Revised:  Here we exhibit an example of a singleton where the iterated hairpin completion is not regular, actually it is not context-free .
Edit intent: clarity
Original:  we show that a natural subset of this set is in bijection with a set of m-clusters (in the cluster algebra sense).
Revised:  we show that a natural subset of these objects is in natural bijection with a set of m-clusters (in the cluster algebra sense).
Edit intent: clarity
Original:  We classify and enumerate these objects and further show that a natural subset of these objects is in natural bijection with a set of m-clusters (in the cluster algebra sense) .
Revised:  We classify and enumerate them and show that a natural subset of these objects is in natural bijection with a set of m-clusters (in the cluster algebra sense) .
Edit intent: clarity
Original:  We classify and enumerate these objects and further show that a natural subset of these objects is in natural bijection with a set of m-clusters (in the cluster algebra sense) .
Revised:  We classify and enumerate these objects and further show that a natural subset is in bijection with a set of m-clusters (in the cluster algebra sense) .
Edit intent: clarity
Original:  These are generalisations of objects arising from interval exchange transformations generalising those in the Sturmian context .
Revised:  These are generalizations of objects arising from interval exchange transformations generalising those in the Sturmian context .
Edit intent: fluency
Original:  Furthermore, we interpret a notion of induction used to model generalised interval exchange transformations as a composition of cluster mutations .
Revised:  Furthermore, we interpret a notion of induction used to model generalised interval exchange transformations .
Edit intent: clarity
Original:  This paper captures the attributes of creation times of purchasing orders to an individual vendor, as well as to all vendors, and further investigates whether they have some kind of dynamics by applying logarithmic binning to the construction of distribution plot.
Revised:  This paper captures the attributes of creation times of purchase orders to an individual vendor, as well as to all vendors, and further investigates whether they have some kind of dynamics by applying logarithmic binning to the construction of distribution plot.
Edit intent: fluency
Original:  To better describe the mechanism generating the heterogeneity of purchasing order assignment process from the objective company to all its vendors, a model driven by product life cycle is introduced, and then the analytical distribution and the simulation result are obtained, which are in good line with the empirical data.
Revised:  To better describe the mechanism generating the heterogeneity of purchase order assignment process from the objective company to all its vendors, a model driven by product life cycle is introduced, and then the analytical distribution and the simulation result are obtained, which are in good line with the empirical data.
Edit intent: fluency
Original:  Special attention has been spent on the characteristics of the local ordering of water molecules around these compatible solutes .
Revised:  Special attention has been spent on the local surrounding structure of water molecules around these compatible solutes .
Edit intent: clarity
Original:  Special attention has been spent on the characteristics of the local ordering of water molecules around these compatible solutes .
Revised:  Special attention has been spent on the characteristics of the local ordering of water molecules .
Edit intent: clarity
Original:  Our results indicate that ectoine and hydroxyectoine are able to bind more water molecules than urea on short scales.
Revised:  Our results indicate that ectoine and hydroxyectoine are able to accumulate more water molecules than urea on short scales.
Edit intent: clarity
Original: This paper deals with the containment problem under homothetics , a generalization of the minimal enclosing ball problem.
Revised: This paper deals with the containment problem under homothetics which has the minimal enclosing ball problem.
Edit intent: clarity
Original:  In the case where the asset is driven by Brownian motion, an associated "master equation" for the dynamics of the conditional probability density is derived and expressed in integral form.
Revised:  In the case where the price process is driven by Brownian motion, an associated "master equation" for the dynamics of the conditional probability density is derived and expressed in integral form.
Edit intent: clarity
Original:  We show that uncertainty can be controlled in large part by trading off coupling strength among multiple neural populations against the noise amplitude.
Revised:  We show that uncertainty can be controlled in large part by trading off synchronization strength among multiple neural populations against the noise amplitude.
Edit intent: clarity
Original:  We show that uncertainty can be controlled in large part by trading off coupling strength among multiple neural populations against the noise amplitude.
Revised:  We show that uncertainty can be controlled in large part by trading off coupling strength among multiple redundant neural systems against the noise amplitude.
Edit intent: clarity
Original:  Simulations comparing theoretical bounds to the relevant empirical quantities show that the estimates can be tight.
Revised:  Simulations comparing theoretical bounds to the relevant empirical quantities show that the theoretical estimates we derive can be tight.
Edit intent: clarity
Original:  Previous applications of the algorithm have yielded large efficiency gains over other sampling techniques  including parallel tempering.
Revised:  Previous applications of the algorithm have yielded large efficiency gains over other sampling techniques , including parallel tempering.
Edit intent: fluency
Original: Nested sampling is a  technique developed to explore probability distributions localised in an exponentially small area of the parameter space.
Revised: Nested sampling is a technique developed to explore probability distributions lo- calised in an exponentially small area of the parameter space.
Edit intent: fluency
Original: We show that a careful analysis of co-authorship in publications within a discipline uncovers interesting properties of the analysed field.
Revised: Co-authorship in publications within a discipline uncovers interesting properties of the analysed field.
Edit intent: coherence
Original:  We build the largest collaboration network for computer science ever studied, as well as those sub-networks that emerge from conference and journal co-authorship only.
Revised:  We represent collaboration in academic papers of computer science in terms of differently grained networks, including those sub-networks that emerge from conference and journal co-authorship only.
Edit intent: clarity
Original: The main aim of the paper is to present a proof of the decidability of language equivalence for deterministic pushdown automata, which is the famous problem solved by G. Senizergues , for which C. Stirling has also derived a primitive recursive complexity upper bound later.
Revised: The main aim of the paper is to present a proof of the decidability of language equivalence for deterministic pushdown automata, which is the famous problem solved by G. S\'enizergues , for which C. Stirling has also derived a primitive recursive complexity upper bound later.
Edit intent: fluency
Original:  The proof presented here is intended to be  easily understandable, to use simple ideas, and to avoid technicalities when possible.
Revised:  The proof presented here is intended to be easily understandable, and to avoid technicalities when possible.
Edit intent: clarity
Original:  It is illuminated by a fictional Attacker-Defender game, which also allows to develop an intuition for a sketch of a possible extension to bisimilarity for nondeterministic pushdown automata with restricted use of epsilon-steps (a problem, for which the first proof was also given by G. Senizergues) .
Revised:  It is illuminated by a fictional Attacker-Defender game, which is also aimed at developing intuition for a sketch of a possible extension to bisimilarity for nondeterministic pushdown automata with restricted use of epsilon-steps (a problem, for which the first proof was also given by G. Senizergues) .
Edit intent: clarity
Original:  The framework of (deterministic) 1st order grammars has turned out particularly useful to this aim .
Revised:  The framework of (deterministic) 1st order grammars .
Edit intent: clarity
Original: The main aim of the paper is to present a proof of the decidability of language equivalence for deterministic pushdown automata, which is the famous problem solved by G. S\'enizergues , for which C. Stirling has also derived a primitive recursive complexity upper bound later .
Revised: The main aim of the paper is to present a proof of the decidability of language equivalence for deterministic pushdown automata, which is the famous problem solved by G. Senizergues , for which C. Stirling has also derived a primitive recursive complexity upper bound later .
Edit intent: fluency
Original: The main aim of the paper is to present a proof of the decidability of language equivalence for deterministic pushdown automata, which is the famous problem solved by G. S\'enizergues , for which C. Stirling has also derived a primitive recursive complexity upper bound later .
Revised: The main aim of the paper is to present a proof of the decidability of language equivalence for deterministic pushdown automata, which is the famous problem solved by G. S\'enizergues , for which C. Stirling has derived a primitive recursive complexity upper bound later .
Edit intent: clarity
Original: The main aim of the paper is to present a proof of the decidability of language equivalence for deterministic pushdown automata, which is the famous problem solved by G. S\'enizergues , for which C. Stirling has also derived a primitive recursive complexity upper bound later .
Revised: The main aim of the paper is to present a proof of the decidability of language equivalence for deterministic pushdown automata, which is the famous problem solved by G. S\'enizergues , for which C. Stirling has also derived a primitive recursive complexity upper bound .
Edit intent: coherence
Original:  We note that the above bisimulation equivalence result is more-or-less equivalent to the decidability result for nondeterministic pushdown automata with restricted use of epsilon-steps, for which the first proof was also given by G. S\'enizergues .
Revised:  The above bisimulation equivalence result is more-or-less equivalent to the decidability result for nondeterministic pushdown automata with restricted use of epsilon-steps, for which the first proof was also given by G. S\'enizergues .
Edit intent: coherence
Original:  Finally, an appendix presents a modification of Stirling's approach, yielding a complexity bound in the deterministic case which is of the form tetr(2,g(n)) where tetr is the (nonelementary) operator of iterated exponentiation (tetration) and g is an elementary function of the input size.
Revised:  Finally, an appendix presents a modification of Stirling's approach, yielding a complexity bound of the form tetr(2,g(n)) where tetr is the (nonelementary) operator of iterated exponentiation (tetration) and g is an elementary function of the input size.
Edit intent: coherence
Original:  Increasingly, however, communication links are  operating at shorter ranges where transmit power can drop below the power consumed in decoding.
Revised:  However, communication links are operating at shorter ranges where transmit power can drop below the power consumed in decoding.
Edit intent: clarity
Original:  Increasingly, however, communication links are  operating at shorter ranges where transmit power can drop below the power consumed in decoding.
Revised:  Increasingly, however, communication links are increasingly operating at shorter ranges where transmit power can drop below the power consumed in decoding.
Edit intent: clarity
Original:  In this paper , we model the required decoding power and investigate the minimization of total system power from two complementary perspectives.
Revised:  This paper models the required decoding power and investigate the minimization of total system power from two complementary perspectives.
Edit intent: fluency
Original:  In this paper , we model the required decoding power and investigate the minimization of total system power from two complementary perspectives.
Revised:  In this paper , we model the required decoding power and investigates the minimization of total system power from two complementary perspectives.
Edit intent: fluency
Original:  2) unlike the implications of the traditional ``waterfall'' curve which focuses on transmit power, the total power must diverge to infinity as error probability goes to zero;
Revised:  2) unlike the implications of the traditional "waterfall" curve which focuses on transmit power, the total power must diverge to infinity as error probability goes to zero;
Edit intent: fluency
Original:  3) Regular LDPCs, and not their  capacity-achieving  counterparts, can be shown to be power order optimal in some cases;
Revised:  3) Regular LDPCs, and not their known capacity-achieving counterparts, can be shown to be power order optimal in some cases;
Edit intent: clarity
Original:  Second, we consider a collection of point-to-point links.
Revised:  Second, we consider a collection of links.
Edit intent: clarity
Original:  However, at low densities, uncoded transmission may be more power efficient in some cases.
Revised:  However, at low densities, uncoded transmission may be more power-efficient in some cases.
Edit intent: fluency
Original:  To do this  we rely on the theory of infinitesimal generators.
Revised:  To do this , we rely on the theory of infinitesimal generators.
Edit intent: fluency
Original: We present a mathematical study of the order book as a multidimensional continuous-time Markov chain where the order flow is modelled by independent Poisson processes.
Revised: We present a mathematical study of the order book as a multidimensional continuous-time Markov chain where the order flow is modeled by independent Poisson processes.
Edit intent: fluency
Original:  Our aim is to bridge the gap between the microscopic description of price formation (agent-based modelling ), and the Stochastic Differential Equations approach used classically to describe price evolution in macroscopic time scales.
Revised:  Our aim is to bridge the gap between the microscopic description of price formation (agent-based modeling ), and the Stochastic Differential Equations approach used classically to describe price evolution in macroscopic time scales.
Edit intent: fluency
Original:  Our aim is to bridge the gap between the microscopic description of price formation (agent-based modelling ), and the Stochastic Differential Equations approach used classically to describe price evolution in macroscopic time scales.
Revised:  Our aim is to bridge the gap between the microscopic description of price formation (agent-based modelling ), and the Stochastic Differential Equations approach used classically to describe price evolution at macroscopic time scales.
Edit intent: fluency