wanyu/IteraTeR_v2 huggingface dataset:
Original:  the data structure can be created in time O(n\lg (n) \lg( 1/\epsilon%DIFDELCMD < }%%% ) ), the space required is\tilde \tilde O(n \lg( 1 / \epsilon ) ), and the query time is  O(n^{1/2+ \epsilon }) . Previous data structures by Fakcharoenphol and Rao (JCSS'06), Klein, Mozes, and Weimann (TransAlg'10), and Mozes and Wulff-Nilsen (ESA'10) with query time\tilde O(n ^{1/2\lg^2n) use space at least \Omega(n\lg n/\lg\lg n).
Revised:  the data structure can be created in time O(n\lg (n) \lg( 1/\epsilon%DIFDELCMD < }%%% ) ), the space required is\tilde \tilde O(n \lg( / \epsilon ) ), and the query time is O(n^{1/2+ \epsilon }) . Previous data structures by Fakcharoenphol and Rao (JCSS'06), Klein, Mozes, and Weimann (TransAlg'10), and Mozes and Wulff-Nilsen (ESA'10) with query time\tilde O(n ^{1/2\lg^2n) use space at least \Omega(n\lg n/\lg\lg n).
Edit intent: coherence
Original:  the data structure can be created in time O(n\lg (n) \lg( 1/\epsilon%DIFDELCMD < }%%% ) ), the space required is\tilde \tilde O(n \lg( 1 / \epsilon ) ), and the query time is  O(n^{1/2+ \epsilon }) . Previous data structures by Fakcharoenphol and Rao (JCSS'06), Klein, Mozes, and Weimann (TransAlg'10), and Mozes and Wulff-Nilsen (ESA'10) with query time\tilde O(n ^{1/2\lg^2n) use space at least \Omega(n\lg n/\lg\lg n).
Revised:  the data structure can be created in time O(n\lg (n) \lg( 1/\epsilon%DIFDELCMD < }%%% ) ), the space required is\tilde \tilde O(n \lg( 1 / ) ), and the query time is O(n^{1/2+ \epsilon }) . Previous data structures by Fakcharoenphol and Rao (JCSS'06), Klein, Mozes, and Weimann (TransAlg'10), and Mozes and Wulff-Nilsen (ESA'10) with query time\tilde O(n ^{1/2\lg^2n) use space at least \Omega(n\lg n/\lg\lg n).
Edit intent: fluency
Original:  the data structure can be created in time O(n\lg (n) \lg( 1/\epsilon%DIFDELCMD < }%%% ) ), the space required is\tilde \tilde O(n \lg( 1 / \epsilon ) ), and the query time is  O(n^{1/2+ \epsilon }) . Previous data structures by Fakcharoenphol and Rao (JCSS'06), Klein, Mozes, and Weimann (TransAlg'10), and Mozes and Wulff-Nilsen (ESA'10) with query time\tilde O(n ^{1/2\lg^2n) use space at least \Omega(n\lg n/\lg\lg n).
Revised:  the data structure can be created in time O(n\lg (n) \lg( 1/\epsilon%DIFDELCMD < }%%% ) ), the space required is\tilde \tilde O(n \lg( 1 / \epsilon ) ), and the query time is O(n^{1/2+ eps }) . Previous data structures by Fakcharoenphol and Rao (JCSS'06), Klein, Mozes, and Weimann (TransAlg'10), and Mozes and Wulff-Nilsen (ESA'10) with query time\tilde O(n ^{1/2\lg^2n) use space at least \Omega(n\lg n/\lg\lg n).
Edit intent: clarity
Original:  the data structure can be created in time O(n\lg (n) \lg( 1/\epsilon%DIFDELCMD < }%%% ) ), the space required is\tilde \tilde O(n \lg( 1 / \epsilon ) ), and the query time is  O(n^{1/2+ \epsilon }) . Previous data structures by Fakcharoenphol and Rao (JCSS'06), Klein, Mozes, and Weimann (TransAlg'10), and Mozes and Wulff-Nilsen (ESA'10) with query time\tilde O(n ^{1/2\lg^2n) use space at least \Omega(n\lg n/\lg\lg n).
Revised:  the data structure can be created in time O(n\lg (n) \lg( 1/\epsilon%DIFDELCMD < }%%% ) ), the space required is\tilde \tilde O(n \lg( 1 / \epsilon ) ), and the query time is O(n^{1/2+ \epsilon }) . Previous data structures by Fakcharoenphol and Rao (JCSS'06), Klein, Mozes, and Weimann (TransAlg'10), and Mozes and Wulff-Nilsen (ESA'10) with query time\tilde O(n \lg^2n) use space at least \Omega(n\lg n/\lg\lg n).
Edit intent: clarity
Original: 5}n) timeper query . Cabello (} SODA' 06)gave a comparable construction for the smaller range S\in n^{4/3\lg^{1/3}n, n^2}%DIFDELCMD < ]%%% . For the range S\in(n\lg n, n^{4/3\lg^{1/3}n), only data structures of size O(S) with query time O(n^2/S) had been known (Djidjev , }  WG'96) . Combined,our results give the best query times for any shortest-path data structure for planar graphs with space S= o(n^{4/3\lg^{1/3}n).
Revised: 5}n) timeper query . Cabello (} SODA' n^{4/3\lg^{1/3}n, n^2}%DIFDELCMD < ]%%% . For the range S\in(n\lg n, n^{4/3\lg^{1/3}n), only data structures of size O(S) with query time O(n^2/S) had been known (Djidjev , } WG'96) . Combined,our results give the best query times for any shortest-path data structure for planar graphs with space S= o(n^{4/3\lg^{1/3}n).
Edit intent: clarity
Original: 5}n) timeper query . Cabello (} SODA' 06)gave a comparable construction for the smaller range S\in n^{4/3\lg^{1/3}n, n^2}%DIFDELCMD < ]%%% . For the range S\in(n\lg n, n^{4/3\lg^{1/3}n), only data structures of size O(S) with query time O(n^2/S) had been known (Djidjev , }  WG'96) . Combined,our results give the best query times for any shortest-path data structure for planar graphs with space S= o(n^{4/3\lg^{1/3}n).
Revised: 5}n) timeper query . Cabello (} SODA' 06)gave a comparable construction for the smaller range S\in \lg^{1/3}n, n^2}%DIFDELCMD < ]%%% . For the range S\in(n\lg n, n^{4/3\lg^{1/3}n), only data structures of size O(S) with query time O(n^2/S) had been known (Djidjev , } WG'96) . Combined,our results give the best query times for any shortest-path data structure for planar graphs with space S= o(n^{4/3\lg^{1/3}n).
Edit intent: fluency
Original: 5}n) timeper query . Cabello (} SODA' 06)gave a comparable construction for the smaller range S\in n^{4/3\lg^{1/3}n, n^2}%DIFDELCMD < ]%%% . For the range S\in(n\lg n, n^{4/3\lg^{1/3}n), only data structures of size O(S) with query time O(n^2/S) had been known (Djidjev , }  WG'96) . Combined,our results give the best query times for any shortest-path data structure for planar graphs with space S= o(n^{4/3\lg^{1/3}n).
Revised: 5}n) timeper query . Cabello (} SODA' 06)gave a comparable construction for the smaller range S\in n^{4/3\lg^{1/3}n, n^2}%DIFDELCMD < ]%%% \lg^{1/3}n), only data structures of size O(S) with query time O(n^2/S) had been known (Djidjev , } WG'96) . Combined,our results give the best query times for any shortest-path data structure for planar graphs with space S= o(n^{4/3\lg^{1/3}n).
Edit intent: coherence
Original: 5}n) timeper query . Cabello (} SODA' 06)gave a comparable construction for the smaller range S\in n^{4/3\lg^{1/3}n, n^2}%DIFDELCMD < ]%%% . For the range S\in(n\lg n, n^{4/3\lg^{1/3}n), only data structures of size O(S) with query time O(n^2/S) had been known (Djidjev , }  WG'96) . Combined,our results give the best query times for any shortest-path data structure for planar graphs with space S= o(n^{4/3\lg^{1/3}n).
Revised: 5}n) timeper query . Cabello (} SODA' 06)gave a comparable construction for the smaller range S\in n^{4/3\lg^{1/3}n, n^2}%DIFDELCMD < ]%%% . For the range S\in(n\lg n, n^{4/3\lg^{1/3}n), only data structures of size O(S) with query time O(n^2/S) had been known (Djidjev , } WG'96) . Combined,our results give the best query times for any shortest-path data structure for planar graphs with space S= \lg^{1/3}n).
Edit intent: clarity
Original: The aim of this paper is to show how option prices in the Jump-diffusion model can be computed using meshless methods based on Radial Basis Function (RBF) interpolation.
Revised: The aim of this paper is to show how option prices in jump-diffusion models can be computed using meshless methods based on Radial Basis Function (RBF) interpolation.
Edit intent: fluency
Original:  Moreover, the solution functions of the PIDE are approximated explicitly by RBFs which have exact forms so we can easily compute the global intergal by any kind of numerical quadrature.
Revised:  Moreover, the solution functions of the PIDE are approximated explicitly by RBFs which have exact forms so we can easily compute the global integral by any kind of numerical quadrature.
Edit intent: fluency
Original:  Finally, we will also show numerically that our scheme is second order accurate in spatial variables in both American and European cases .
Revised:  Finally, we will not only show numerically that our scheme is second order accurate in spatial variables in both American and European cases .
Edit intent: coherence
Original:  Our approach may be seen as a derandomization of ` sieve' algorithms for exact SVP and CVP (Ajtai, Kumar, and Sivakumar;
Revised:  Our approach may be seen as a derandomization of ' sieve' algorithms for exact SVP and CVP (Ajtai, Kumar, and Sivakumar;
Edit intent: fluency
Original:  We also give an algorithm for solving the exact Closest Vector Problem in 2 ^O(n) time and space, when the target point is within any constant factor of the minimum distance of the lattice.
Revised:  We also give an algorithm for solving the exact Closest Vector Problem in 2 ^{O(n) when the target point is within any constant factor of the minimum distance of the lattice.
Edit intent: clarity
Original:  Our approach may be seen as a derandomization of 'sieve' algorithms for exact SVP and CVP (Ajtai, Kumar, and Sivakumar;
Revised:  Our approach may be seen as a derandomization of the "AKS sieve" for exact SVP and CVP (Ajtai, Kumar, and Sivakumar;
Edit intent: clarity
Original:  In this model, a photon is a processing wave front instantiated from an entity program class, and quantum collapse is when one class stops to merge with another, which restarts its processing .
Revised:  In this model, a photon is an entity program class, and quantum collapse is when one class stops to merge with another, which restarts its processing .
Edit intent: clarity
Original:  Its conceptual cost is that physical reality becomes a processing output .
Revised:  The conceptual cost is that physical reality becomes a processing output .
Edit intent: fluency
Original: The behavior of mobile agents has received recently wide attention  .
Revised: The patterns of motion of mobile agents has received recently wide attention .
Edit intent: clarity
Original:  Special emphasis has been taken in the statistical distribution of the distances that such agents cover .
Revised:  Special attention has been given to the covered distances statistical distributions .
Edit intent: clarity
Original:  In some cases  due to the lack of accurate data about the mobility of the agents , very ingenious and original experiments have been designed.
Revised:  In some cases , due to the lack of accurate data about the mobility of the agents , very ingenious and original experiments have been designed.
Edit intent: fluency
Original:  In some cases  due to the lack of accurate data about the mobility of the agents , very ingenious and original experiments have been designed.
Revised:  In some cases due to the lack of accurate data about the motion of the agents , very ingenious and original experiments have been designed.
Edit intent: fluency
Original:  In these experiments , loosely speaking, is intended to infer the real motion of the agents  from the observed position of them at several consecutives positions with observation times taken from a known or assumed distribution .
Revised:  In these experiments , loosely speaking, is intended to infer the statistical properties of the agents from the observed position of them at several consecutives positions with observation times taken from a known or assumed distribution .
Edit intent: clarity
Original:  The aim of this paper is to show that , at least for a Gaussian random walker, the distribution of the distances between observed positions is conditioned by the distribution of the observation times.
Revised:  The aim of this work is to demonstrate that for a Gaussian random walker, the distribution of the distances between observed positions is conditioned by the distribution of the observation times.
Edit intent: clarity
Original: In this paper we present a modified FPC-BB algorithm for solving the minimum-rank Gram matrix completion problem , i.e., computing a representation for a positive semidefinite polynomial as a sum of minimum number of squares of polynomials in Q x_1,. .., x_s%DIFDELCMD < ]%%% . We prove the convergence of the algorithm under some conditions.
Revised: The problem of computing a representation for a positive semidefinite polynomial as a sum of minimum number of squares of polynomials in Q x_1,. .., x_s%DIFDELCMD < ]%%% . We prove the convergence of the algorithm under some conditions.
Edit intent: clarity
Original: In this paper we present a modified FPC-BB algorithm for solving the minimum-rank Gram matrix completion problem , i.e., computing a representation for a positive semidefinite polynomial as a sum of minimum number of squares of polynomials in Q x_1,. .., x_s%DIFDELCMD < ]%%% . We prove the convergence of the algorithm under some conditions.
Revised: In this paper we present a modified FPC-BB algorithm for solving the minimum-rank Gram matrix completion problem , i.e., computing a representation for a positive semidefinite polynomial as a sum of minimum number of squares of polynomials x_1,. .., x_s%DIFDELCMD < ]%%% . We prove the convergence of the algorithm under some conditions.
Edit intent: coherence
Original:  We simulate several options to design MBMP and compare the performances of these options through mathematical analysis and simulation results, and compare its effectiveness with the existing admission control schemes through extensive simulations. KEYWORDS
Revised:  We simulate several options to design MBMP and compare the performances of these options through mathematical analysis and simulation results, and compare its effectiveness with the existing admission control schemes through extensive simulations. 
Edit intent: coherence
Original: The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems -- delay-tolerant networks, opportunistic-mobility networks, social networks -- obtaining closely related insights.
Revised: The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems - delay-tolerant networks, opportunistic-mobility networks, social networks -- obtaining closely related insights.
Edit intent: fluency
Original: The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems -- delay-tolerant networks, opportunistic-mobility networks, social networks -- obtaining closely related insights.
Revised: The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems -- delay-tolerant networks, opportunistic-mobility networks, social networks - obtaining closely related insights.
Edit intent: fluency
Original:  The main contribution of this paper is to integrate the existing partial models proposed in the literature into a unified framework, which we call TVG (for time-varying graphs).
Revised:  The main contribution of this paper is to integrate the vast collection of concepts, formalisms, and results found in the literature into a unified framework, which we call TVG (for time-varying graphs).
Edit intent: clarity
Original:  As part of the framework definition, we identify a hierarchy of classes of TVGs , defined with respects to basic properties to which correspond necessary conditions and impossibility results for basic computations;
Revised:  As part of the framework definition, we identify a hierarchy of classes of TVGs defined with respects to basic properties to which correspond necessary conditions and impossibility results for basic computations;
Edit intent: fluency
Original: The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems - delay-tolerant networks, opportunistic-mobility networks, social networks - obtaining closely related insights.
Revised: The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems -- delay-tolerant networks, opportunistic-mobility networks, social networks - obtaining closely related insights.
Edit intent: fluency
Original: The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems - delay-tolerant networks, opportunistic-mobility networks, social networks - obtaining closely related insights.
Revised: The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems - delay-tolerant networks, opportunistic-mobility networks, social networks -- obtaining closely related insights.
Edit intent: fluency
Original:  and the formal models proposed so far to express some specific concepts can be viewed as fragments of a larger formal description of this universe.
Revised:  and the formal models proposed so far to express some specific concepts are components of a larger formal description of this universe.
Edit intent: clarity
Original:  Besides this definitional work, we articulate both existing works and original suggestions around three main federative motifs.
Revised:  Based on this definitional work, we articulate both existing works and original suggestions around three main federative motifs.
Edit intent: coherence
Original: As the pricing mechanism in more than half the world's financial markets, the limit order book has recently been the focus of a great deal of published literature in a wide range of disciplines .
Revised: As the pricing mechanism in more than half the world's financial markets, limit order books have featured extensively in the published literature from a wide range of disciplines .
Edit intent: clarity
Original:  In this survey , we present a mathematical description of the price matching algorithm at the heart of limit order trading, and highlight some of the key publications - both empirical and theoretical - that have advanced understanding of the process to date.
Revised:  In this survey , we present a mathematical description of the price matching algorithm at the heart of limit order trading, and highlight some of the key publications - both empirical and theoretical publications that have advanced understanding of the process to date.
Edit intent: style
Original:  In this survey , we present a mathematical description of the price matching algorithm at the heart of limit order trading, and highlight some of the key publications - both empirical and theoretical - that have advanced understanding of the process to date.
Revised:  In this survey , we present a mathematical description of the price matching algorithm at the heart of limit order trading, and highlight some of the key publications - both empirical and theoretical - that have advanced understanding of limit order books to date.
Edit intent: clarity
Original:   By examining existing models of limit order markets , we identify some of the key unresolved questions and difficulties facing researchers of limit order trading today.
Revised:  By examining existing limit order book models , we identify some of the key unresolved questions and difficulties facing researchers of limit order trading today.
Edit intent: clarity
Original:   By examining existing models of limit order markets , we identify some of the key unresolved questions and difficulties facing researchers of limit order trading today.
Revised:  By examining existing models of limit order markets , we identify the key unresolved questions and difficulties facing researchers of limit order trading today.
Edit intent: clarity
Original: As the pricing mechanism in more than half  the world's financial markets, limit order books have featured extensively in the published literature from a wide range of disciplines over the past decade.
Revised: Limit order books are used to match buyers and sellers in more than half the world's financial markets, limit order books have featured extensively in the published literature from a wide range of disciplines over the past decade.
Edit intent: clarity
Original: As the pricing mechanism in more than half  the world's financial markets, limit order books have featured extensively in the published literature from a wide range of disciplines over the past decade.
Revised: As the pricing mechanism in more than half of the world's financial markets, limit order books have featured extensively in the published literature from a wide range of disciplines over the past decade.
Edit intent: fluency
Original: As the pricing mechanism in more than half  the world's financial markets, limit order books have featured extensively in the published literature from a wide range of disciplines over the past decade.
Revised: As the pricing mechanism in more than half the world's financial markets, and have been studied extensively in several disciplines during the past decade.
Edit intent: clarity
Original:  Despite clear advances, a substantial chasm still remains between observations from empirical studies of limit order books and  models that attempt to replicate them.
Revised:  Despite clear advances, a substantial chasm still remains between observations from empirical studies of limit order books and the models that attempt to replicate them.
Edit intent: fluency
Original:  In particular, many modelling assumptions are poorly supported by data , and several well-established empirical facts remain absent from model outputs .
Revised:  In particular, many modelling assumptions are poorly supported by data and several well-established empirical facts remain absent from model outputs .
Edit intent: fluency
Original:  In particular, many modelling assumptions are poorly supported by data , and several well-established empirical facts remain absent from model outputs .
Revised:  In particular, many modelling assumptions are poorly supported by data , and several well-established empirical facts have yet to be reproduced satisfactorily by models .
Edit intent: clarity
Original:  By examining existing limit order book models , we identify the key unresolved questions and difficulties facing researchers of limit order trading today .
Revised:  By examining existing models of limit order books , we identify the key unresolved questions and difficulties facing researchers of limit order trading today .
Edit intent: fluency
Original:  By examining existing limit order book models , we identify the key unresolved questions and difficulties facing researchers of limit order trading today .
Revised:  By examining existing limit order book models , we identify some key unresolved questions and difficulties facing researchers of limit order trading today .
Edit intent: clarity
Original:  By examining existing limit order book models , we identify the key unresolved questions and difficulties facing researchers of limit order trading today .
Revised:  By examining existing limit order book models , we identify the key unresolved questions and difficultes currently facing researchers of limit order trading today .
Edit intent: clarity
Original:  By examining existing limit order book models , we identify the key unresolved questions and difficulties facing researchers of limit order trading today .
Revised:  By examining existing limit order book models , we identify the key unresolved questions and difficulties facing researchers of limit order trading .
Edit intent: clarity
Original: Limit order books are used to match buyers and sellers in more than half of the world's financial markets , and have been studied extensively in several disciplines during the past decade .
Revised: Limit order books (LOBs) match buyers and sellers in more than half of the world's financial markets , and have been studied extensively in several disciplines during the past decade .
Edit intent: clarity
Original: Limit order books are used to match buyers and sellers in more than half of the world's financial markets , and have been studied extensively in several disciplines during the past decade .
Revised: Limit order books are used to match buyers and sellers in more than half of the world's financial markets .
Edit intent: clarity
Original:  This survey highlights the many insights from the wealth of empricial and theoretical studies that have been conducted, and the numerous unsolved problems that remain.
Revised:  This survey highlights the insights that have emerged from the wealth of empricial and theoretical studies that have been conducted, and the numerous unsolved problems that remain.
Edit intent: clarity