wanyu/IteraTeR_v2 huggingface dataset:
Original:  Let \Gamma be a Cayley graph of the symmetric group on n letters generated by a transposition tree T . In \mbox{ Akers:Krishnamurthy:19890pt \mbox{ Hahn:Sabidussi:1997}0pt } 0pt (see also \mbox{ Hahn:Sabidussi:1997}0pt )} , it is shown that the diameter of  \Gamma is bounded as \diam(\Gamma) \le \max \SUBSCRIPT  \pi \in S_n%DIFDELCMD < \MBLOCKRIGHTBRACE %DIFDELCMD < {%%% c(\pi) -
Revised:  Let \Gamma be a Cayley graph of the permutation group generated by a transposition tree T . In \mbox{ Akers:Krishnamurthy:19890pt \mbox{ Hahn:Sabidussi:1997}0pt } 0pt (see also \mbox{ Hahn:Sabidussi:1997}0pt )} , it is shown that the diameter of \Gamma is bounded as \diam(\Gamma) \le \max \SUBSCRIPT \pi \in S_n%DIFDELCMD < \MBLOCKRIGHTBRACE %DIFDELCMD < {%%% c(\pi) -
Edit intent: clarity
Original:  Let \Gamma be a Cayley graph of the symmetric group on n letters generated by a transposition tree T . In \mbox{ Akers:Krishnamurthy:19890pt \mbox{ Hahn:Sabidussi:1997}0pt } 0pt (see also \mbox{ Hahn:Sabidussi:1997}0pt )} , it is shown that the diameter of  \Gamma is bounded as \diam(\Gamma) \le \max \SUBSCRIPT  \pi \in S_n%DIFDELCMD < \MBLOCKRIGHTBRACE %DIFDELCMD < {%%% c(\pi) -
Revised:  Let \Gamma be a Cayley graph of the symmetric group on n letters generated by a transposition tree T . In \mbox{ Akers:Krishnamurthy:19890pt \mbox{ Hahn:Sabidussi:1997}0pt } 0pt (see also \mbox{ Hahn:Sabidussi:1997}0pt )} , it is shown that the diameter of the Cayley graph \Gamma is bounded as \diam(\Gamma) \le \max \SUBSCRIPT \pi \in S_n%DIFDELCMD < \MBLOCKRIGHTBRACE %DIFDELCMD < {%%% c(\pi) -
Edit intent: fluency
Original: n+\sum_{i=1}^n \dist _T(i, \pi (i)) , where  c(\pi) denotes the number of cycles in \pi, and \dist_T is the distance function in T.
Revised: n+\sum_{i=1}^n \dist _T(i, \pi (i)) , where c(\pi) denotes the number of cycles in \pi, and \dist_T is the distance function in T.
Edit intent: fluency
Original: n+\sum_{i=1}^n \dist _T(i, \pi (i)) , where  c(\pi) denotes the number of cycles in \pi, and \dist_T is the distance function in T.
Revised: n+\sum_{i=1}^n \dist _T(i, \pi , where c(\pi) denotes the number of cycles in \pi, and \dist_T is the distance function in T.
Edit intent: clarity
Original:  In this work, we assess the sharpness and strictness  of this upper bound.
Revised:  In this work, we assess the sharpness and strictness ) of this upper bound.
Edit intent: fluency
Original:  We show that the upper bound is exact for all trees of maximum diameter and also for all trees of minimum diameter, and we exhibit some families of trees (that are non-extremal) for which the bound is strict.
Revised:  We show that the upper bound is sharp for all trees of maximum diameter and also for all trees of minimum diameter, and we exhibit some families of trees (that are non-extremal) for which the bound is strict.
Edit intent: clarity
Original:  We show that the upper bound is exact for all trees of maximum diameter and also for all trees of minimum diameter, and we exhibit some families of trees (that are non-extremal) for which the bound is strict.
Revised:  We show that the upper bound is exact for all trees of maximum diameter and also for all trees of minimum diameter, and we exhibit some families of trees for which the bound is strict.
Edit intent: coherence
Original:  We then show that for every n, there exists a tree on n vertices, such that the difference between the upper bound and the actual diameter is at least n-4 \diam\le \le  ^n}\dist .
Revised:  We then show that for every n, there exists a tree on n vertices, such that the difference between the upper bound and the true diameter value is at least n-4 \diam\le \le ^n}\dist .
Edit intent: clarity
Original: This work concerns the problem of determining or estimating the diameter of some families of Cayley networks.
Edit intent: coherence
Original:  For all families of trees examined so far, the value \beta computed by our algorithm happens to also be an upper bound on the diameter, i.e. \diam(\Gamma) \le \beta \le \max \SUBSCRIPT  \pi \in S_n%DIFDELCMD < \MBLOCKRIGHTBRACE {%%% c(\pi) -n+i=1^n \dist _T(i,\pi(i)) .
Revised:  For all families of trees examined so far, the value \beta computed by our algorithm happens to also be an upper bound on the diameter, i.e. \diam(\Gamma) \le \beta \le \max \SUBSCRIPT \pi %DIFDELCMD < \MBLOCKRIGHTBRACE {%%% c(\pi) -n+i=1^n \dist _T(i,\pi(i)) .
Edit intent: clarity
Original:  For all families of trees examined so far, the value \beta computed by our algorithm happens to also be an upper bound on the diameter, i.e. \diam(\Gamma) \le \beta \le \max \SUBSCRIPT  \pi \in S_n%DIFDELCMD < \MBLOCKRIGHTBRACE {%%% c(\pi) -n+i=1^n \dist _T(i,\pi(i)) .
Revised:  For all families of trees examined so far, the value \beta computed by our algorithm happens to also be an upper bound on the diameter, i.e. \diam(\Gamma) \le \beta \le \max \SUBSCRIPT \pi \in S_n%DIFDELCMD < \MBLOCKRIGHTBRACE {%%% c(\pi) -n+i=1^n \dist _T(i,\pi(i)) .
Edit intent: fluency
Original: Many scientists and engineers use Octave or MATLAB as their preferred programming language .
Revised: Although, many scientists and engineers use Octave or MATLAB as their preferred programming language .
Edit intent: coherence
Original:  However , dynamic nature of these languages can lead to slower running-time of programs written in these languages compared to programs written in languages which are not as dynamic, like C, C++ and Fortran.
Revised:  However , dynamic nature of these languages leads to slower running-time of programs written in these languages compared to programs written in languages which are not as dynamic, like C, C++ and Fortran.
Edit intent: coherence
Original:  In this work we have developed a translator for a new programming language (tym) that tries to address performance issues which are common is scientific programs by adding new constructs to  Octave/MATLAB  .
Revised:  In this work we developed a translator for a new programming language (tym) that tries to address performance issues which are common is scientific programs by adding new constructs to Octave/MATLAB .
Edit intent: fluency
Original:  In this work we have developed a translator for a new programming language (tym) that tries to address performance issues which are common is scientific programs by adding new constructs to  Octave/MATLAB  .
Revised:  In this work we have developed a translator for a new programming language (tym) which tries to address performance issues which are common is scientific programs by adding new constructs to Octave/MATLAB .
Edit intent: fluency
Original:  In this work we have developed a translator for a new programming language (tym) that tries to address performance issues which are common is scientific programs by adding new constructs to  Octave/MATLAB  .
Revised:  In this work we have developed a translator for a new programming language (tym) that tries to address performance issues , common in scientific programs, by adding new constructs to Octave/MATLAB .
Edit intent: coherence
Original: Although, many scientists and engineers use Octave or MATLAB as their preferred programming language, dynamic nature of these languages leads to slower running-time of programs written in these languages compared to programs written in languages which are not as dynamic, like C, C++ and Fortran.
Revised: Although, many scientists and engineers use Octave or MATLAB as their preferred programming language, dynamic nature of these languages can lead to slower running-time of programs written in these languages compared to programs written in languages which are not as dynamic, like C, C++ and Fortran.
Edit intent: clarity
Original: We prove that  for locally bounded processes, the absence of arbitrage  of the first kind is equivalent to the existence of a dominating local martingale measure.
Revised: We prove that , for locally bounded processes, the absence of arbitrage of the first kind is equivalent to the existence of a dominating local martingale measure.
Edit intent: fluency
Original: We prove that  for locally bounded processes, the absence of arbitrage  of the first kind is equivalent to the existence of a dominating local martingale measure.
Revised: We prove that for locally bounded processes, absence of arbitrage of the first kind is equivalent to the existence of a dominating local martingale measure.
Edit intent: fluency
Original: We prove that  for locally bounded processes, the absence of arbitrage  of the first kind is equivalent to the existence of a dominating local martingale measure.
Revised: We prove that for locally bounded processes, the absence of arbitrage opportunities of the first kind is equivalent to the existence of a dominating local martingale measure.
Edit intent: clarity
Original:  Further we construct a lossy conductor model to illustrate how to simulate more general material other than traditional PEC or simple dielectrics, by a new conformal FDTD method which main considers the effects of penetrative depth and the distribution of free bulk electric charge and current.
Revised:  Furthermore we construct a lossy conductor model to illustrate how to simulate more general material other than traditional PEC or simple dielectrics, by a new conformal FDTD method which main considers the effects of penetrative depth and the distribution of free bulk electric charge and current.
Edit intent: fluency
Original:  Further we construct a lossy conductor model to illustrate how to simulate more general material other than traditional PEC or simple dielectrics, by a new conformal FDTD method which main considers the effects of penetrative depth and the distribution of free bulk electric charge and current.
Revised:  Further we construct a lossy conductor model to illustrate how to simulate more general materials other than traditional PEC or simple dielectrics, by a new conformal FDTD method which main considers the effects of penetrative depth and the distribution of free bulk electric charge and current.
Edit intent: fluency
Original:  The semantics of a MPM is an infinite- state continuous-time Markov chain.
Revised:  The semantics of a MPM is an infinite-state continuous-time Markov chain.
Edit intent: fluency
Original:  Moreover, the source node and the different storage nodes might not be able to send and receive data simultaneously -e .g., nodes might be busy in a datacenter setting, or simply be offline in a peer-to-peer setting- which can further threaten the efficacy of the overall storage process.
Revised:  Moreover, the source node and the different storage nodes might not be able to send and receive data simultaneously -- e .g., nodes might be busy in a datacenter setting, or simply be offline in a peer-to-peer setting- which can further threaten the efficacy of the overall storage process.
Edit intent: fluency
Original:  Moreover, the source node and the different storage nodes might not be able to send and receive data simultaneously -e .g., nodes might be busy in a datacenter setting, or simply be offline in a peer-to-peer setting- which can further threaten the efficacy of the overall storage process.
Revised:  Moreover, the source node and the different storage nodes might not be able to send and receive data simultaneously -e .g., nodes might be busy in a datacenter setting, or simply be offline in a peer-to-peer setting -- which can further threaten the efficacy of the overall storage process.
Edit intent: fluency
Original: Delay-capacity tradeoffs for mobile networks have been analyzed through a number of research work , but L\'{e}vy mobility  has not been adopted in such research workdue to its mathematical complexity.
Revised: Delay-capacity tradeoffs for mobile networks have been analyzed through a number of research work . However, L\'{e}vy mobility has not been adopted in such research workdue to its mathematical complexity.
Edit intent: coherence
Original:  This paper analytically derives an important point in the delay-capacity tradeoffs , known as critical delay, the minimum delay required to achieve more throughput than \Theta( 1/n) where n is the number of nodes in the network for L\'{e}vy mobility : L\'{e}vy flight and L\'{e}vy walk . L\'{e \alpha \in (0,2] is of special interest because it is known that L\'{evy mobility and human mobility share several common features including heavy-tail step size distributions.
Revised:  This paper analytically derives an important point in the delay-capacity tradeoff for L\'{e , known as critical delay, the minimum delay required to achieve more throughput than \Theta( 1/n) where n is the number of nodes in the network for L\'{e}vy mobility : L\'{e}vy flight and L\'{e}vy walk . L\'{e \alpha \in (0,2] is of special interest because it is known that L\'{evy mobility and human mobility share several common features including heavy-tail step size distributions.
Edit intent: fluency
Original:  This paper analytically derives an important point in the delay-capacity tradeoffs , known as critical delay, the minimum delay required to achieve more throughput than \Theta( 1/n) where n is the number of nodes in the network for L\'{e}vy mobility : L\'{e}vy flight and L\'{e}vy walk . L\'{e \alpha \in (0,2] is of special interest because it is known that L\'{evy mobility and human mobility share several common features including heavy-tail step size distributions.
Revised:  This paper analytically derives an important point in the delay-capacity tradeoffs , known as the critical delay. The critical delay is the minimum delay required to achieve more throughput than \Theta( 1/n) where n is the number of nodes in the network for L\'{e}vy mobility : L\'{e}vy flight and L\'{e}vy walk . L\'{e \alpha \in (0,2] is of special interest because it is known that L\'{evy mobility and human mobility share several common features including heavy-tail step size distributions.
Edit intent: fluency
Original:  This paper analytically derives an important point in the delay-capacity tradeoffs , known as critical delay, the minimum delay required to achieve more throughput than \Theta( 1/n) where n is the number of nodes in the network for L\'{e}vy mobility : L\'{e}vy flight and L\'{e}vy walk . L\'{e \alpha \in (0,2] is of special interest because it is known that L\'{evy mobility and human mobility share several common features including heavy-tail step size distributions.
Revised:  This paper analytically derives an important point in the delay-capacity tradeoffs , known as critical delay, the minimum delay required to achieve more throughput than \Theta( 1/n) per node in a network with n nodes). The L\'{e}vy mobility : L\'{e}vy flight and L\'{e}vy walk . L\'{e \alpha \in (0,2] is of special interest because it is known that L\'{evy mobility and human mobility share several common features including heavy-tail step size distributions.
Edit intent: clarity
Original:  This paper analytically derives an important point in the delay-capacity tradeoffs , known as critical delay, the minimum delay required to achieve more throughput than \Theta( 1/n) where n is the number of nodes in the network for L\'{e}vy mobility : L\'{e}vy flight and L\'{e}vy walk . L\'{e \alpha \in (0,2] is of special interest because it is known that L\'{evy mobility and human mobility share several common features including heavy-tail step size distributions.
Revised:  This paper analytically derives an important point in the delay-capacity tradeoffs , known as critical delay, the minimum delay required to achieve more throughput than \Theta( 1/n) where n is the number of nodes in the network for L\'{e}vy mobility includes L\'{e}vy flight and L\'{e}vy walk . L\'{e \alpha \in (0,2] is of special interest because it is known that L\'{evy mobility and human mobility share several common features including heavy-tail step size distributions.
Edit intent: fluency
Original:  This paper analytically derives an important point in the delay-capacity tradeoffs , known as critical delay, the minimum delay required to achieve more throughput than \Theta( 1/n) where n is the number of nodes in the network for L\'{e}vy mobility : L\'{e}vy flight and L\'{e}vy walk . L\'{e \alpha \in (0,2] is of special interest because it is known that L\'{evy mobility and human mobility share several common features including heavy-tail step size distributions.
Revised:  This paper analytically derives an important point in the delay-capacity tradeoffs , known as critical delay, the minimum delay required to achieve more throughput than \Theta( 1/n) where n is the number of nodes in the network for L\'{e}vy mobility : L\'{e}vy flight and L\'{e}vy walk . L\'{e \alpha \in (0,2] vy mobility and human mobility share several common features including heavy-tail step size distributions.
Edit intent: coherence
Original:  }  Our proposed technique involves an analysis of the joint spatio-temporal probability density function of a time-varying location of a node for L\'{e}vy flight and characterizations of an embedded Markov process in L\'{e}vy walk which is of a semi-Markov process.
Revised:  } Our proposed technique involves an analysis of the joint spatio-temporal probability density function of a time-varying location of a node for L\'{e}vy flight and characterizations of an embedded Markov process in L\'{e}vy walk which is a semi-Markov process.
Edit intent: clarity
Original:  The results indicate that in L\'{e}vy walk, there is a phase transition such that for \alpha \in (0,1), the critical delay is constantly \Theta (n^{1/2}) and for \alpha \in [1,2] it is \Theta(n^{\frac{\alpha}{2}}).
Revised:  The results indicate that in L\'{e}vy walk, there is a phase transition such that for \alpha \in (0,1), the critical delay is always \Theta (n^{1/2}) and for \alpha \in [1,2] it is \Theta(n^{\frac{\alpha}{2}}).
Edit intent: clarity
Original: Influence diffusion and influence maximization in  online social networks (OSNs) have been extensively studied, because it could enable effective viral marketing in large-scale OSNs. However, existing studies have ignored an important aspect of social relationships, namely, relationships may include not only friend relationships but also foe or enemy relationships.
Revised: Influence diffusion and influence maximization in large-scale online social networks (OSNs) have been extensively studied, because it could enable effective viral marketing in large-scale OSNs. However, existing studies have ignored an important aspect of social relationships, namely, relationships may include not only friend relationships but also foe or enemy relationships.
Edit intent: fluency
Original: Influence diffusion and influence maximization in  online social networks (OSNs) have been extensively studied, because it could enable effective viral marketing in large-scale OSNs. However, existing studies have ignored an important aspect of social relationships, namely, relationships may include not only friend relationships but also foe or enemy relationships.
Revised: Influence diffusion and influence maximization in online social networks (OSNs) have been extensively studied, because of their impacts on enabling effective online viral marketing. Existing studies focus on social networks with only friendship relations, whereas the foe or enemy relationships.
Edit intent: clarity
Original:  In this paper, we study influence diffusion and influence maximization in social networks with both positive and negative relationships , which are referred to as signed networks.
Revised:  In this paper, we study influence diffusion and influence maximization in OSNs with both friend and foe relations , which are referred to as signed networks.
Edit intent: clarity
Original:  In this paper, we study influence diffusion and influence maximization in social networks with both positive and negative relationships , which are referred to as signed networks.
Revised:  In this paper, we study influence diffusion and influence maximization in social networks with both positive and negative relationships , which are modeled using positive and negative edges on signed networks.
Edit intent: clarity
Original:  In particular, we extend the classic voter model to signed networks and model the dynamics of influence diffusion of two opposite opinions.
Revised:  In particular, we extend the classic voter model to signed networks and analyze the dynamics of influence diffusion of two opposite opinions.
Edit intent: clarity
Original:  We are able to provide complete characterization of both short-term and long-term dynamics of influence diffusion in this model, and illustrate that the steady state behavior of the dynamics depend on three classes of graph structures, which we refer to as balanced graphs, anti-balanced graphs, and strictly unbalanced graphs.
Revised:  We first provide systematic characterization of both short-term and long-term dynamics of influence diffusion in this model, and illustrate that the steady state behavior of the dynamics depend on three classes of graph structures, which we refer to as balanced graphs, anti-balanced graphs, and strictly unbalanced graphs.
Edit intent: clarity
Original:  We are able to provide complete characterization of both short-term and long-term dynamics of influence diffusion in this model, and illustrate that the steady state behavior of the dynamics depend on three classes of graph structures, which we refer to as balanced graphs, anti-balanced graphs, and strictly unbalanced graphs.
Revised:  We are able to provide complete characterization of both short-term and long-term dynamics of influence diffusion in this model, and illustrate that the steady state behaviors of the dynamics depend on three classes of graph structures, which we refer to as balanced graphs, anti-balanced graphs, and strictly unbalanced graphs.
Edit intent: fluency
Original:  We are able to provide complete characterization of both short-term and long-term dynamics of influence diffusion in this model, and illustrate that the steady state behavior of the dynamics depend on three classes of graph structures, which we refer to as balanced graphs, anti-balanced graphs, and strictly unbalanced graphs.
Revised:  We are able to provide complete characterization of both short-term and long-term dynamics of influence diffusion in this model, and illustrate that the steady state behavior of the dynamics depend on three types of graph structures, which we refer to as balanced graphs, anti-balanced graphs, and strictly unbalanced graphs.
Edit intent: clarity
Original:  We then apply our results to  the influence maximization problem and develop efficient algorithms to select initial seeds of one opinion thats maximizes either its short-term influence coverage or long-term steady state influence coverage.
Revised:  We then apply our results to solve the influence maximization problem and develop efficient algorithms to select initial seeds of one opinion thats maximizes either its short-term influence coverage or long-term steady state influence coverage.
Edit intent: clarity
Original:  We then apply our results to  the influence maximization problem and develop efficient algorithms to select initial seeds of one opinion thats maximizes either its short-term influence coverage or long-term steady state influence coverage.
Revised:  We then apply our results to the influence maximization problem and develop efficient algorithms to select initial seeds of one opinion that maximize either its short-term influence coverage or long-term steady state influence coverage.
Edit intent: fluency