wanyu/IteraTeR_v2 huggingface dataset:
Original:   In general terms the goal is to provide a one-to-one mapping between the vertices of the input graphs such that edge conservationis maximized .
Revised:  In general terms The goal is to provide a one-to-one mapping between the vertices of the input graphs such that edge conservationis maximized .
Edit intent: fluency
Original:   In general terms the goal is to provide a one-to-one mapping between the vertices of the input graphs such that edge conservationis maximized .
Revised:  In general terms the goal is to provide a one-to-one mapping between the vertices of the input graphs in order to maximize edge conservation .
Edit intent: clarity
Original:  Let m_1 (m_2) denote the number of G_2-vertices (G_1-vertices) that each G_1 -vertex (G_2-vertex ) is allowed to be mapped to . All provided results assume m _2=1 , except for the{\em   fixed-parameter tractability result for bounded degree graphs which applies to the more general setting of any constant m_1 , m_2. We present a polynomial time solution for the special case where G_1is acyclic.
Revised:  Let m_1 (m_2) denote the number of G_2-vertices (G_1-vertices) that each G_1 -vertex (G_2-vertex ) is allowed to be mapped to . All provided results assume m _2=1 , except for the{\em conflict graph fixed-parameter tractability result for bounded degree graphs which applies to the more general setting of any constant m_1 , m_2. We present a polynomial time solution for the special case where G_1is acyclic.
Edit intent: fluency
Original:  Our extension to other metric spaces is  based on a supergale characterization of Hausdorff dimension .
Revised:  Our extension to other metric spaces is also based on a supergale characterization of Hausdorff dimension .
Edit intent: clarity
Original:  It is of tutorial nature, and it aims to be an introduction on this topic, providing a clear and easy to follow description.
Revised:  It is of tutorial nature, and it aims to be an introduction on this topic, providing a clear and easy-to-follow description.
Edit intent: fluency
Original:  To illustrate how CTMN can be used, we introduce a set of representative and modern scenarios, such as Vehicular Ad-hoc Networks (VANETs), Power Line Communication networks and multiple overlapping Wireless Local Area Networks (WLANs).
Revised:  To illustrate how CTMN can be used, we introduce a set of representative and cutting-edge scenarios, such as Vehicular Ad-hoc Networks (VANETs), Power Line Communication networks and multiple overlapping Wireless Local Area Networks (WLANs).
Edit intent: clarity
Original:  For each scenario, we describe the specific CTMN, obtain the stationary distribution of the CTMN and compute the throughput achieved by each node in the network.
Revised:  For each scenario, we describe the specific CTMN, obtain its stationary distribution and compute the throughput achieved by each node in the network.
Edit intent: clarity
Original:  Taking the per-node throughput as reference, we discuss how the complex interactions between nodes using CSMA/CA affect the system performance.
Revised:  Taking the per-node throughput as reference, we discuss how the complex interactions between nodes using CSMA/CA have an impact on system performance.
Edit intent: clarity
Original:  It is therefore important for the future of scientific practice to reflect upon the scientists' ethical responsibilities within teams.
Revised:  It is therefore important for the future of scientific practice to reflect upon the individual scientist's ethical responsibilities within teams.
Edit intent: clarity
Original:  A recent set of experiments involving yeast cell populations has shown that selection for larger aggregates leads to the appearance of stable clusters of cells that are able to split into smaller aggregates .
Revised:  A recent set of experiments involving yeast cell populations has shown that selection for larger aggregates leads to the appearance of stable aggregates of cells that are able to split into smaller aggregates .
Edit intent: clarity
Original:  A recent set of experiments involving yeast cell populations has shown that selection for larger aggregates leads to the appearance of stable clusters of cells that are able to split into smaller aggregates .
Revised:  A recent set of experiments involving yeast cell populations has shown that selection for larger aggregates leads to the appearance of stable clusters of cells that are able to split into smaller clusters .
Edit intent: fluency
Original: An  integral quadratic form is a homogeneous polynomial of uniform degree~2 in several variables e.g., an n-ary integral quadratic form in variables x_1, \cdots ,x_n looks like \sum _{1\leq i,j\leq n}a_{ij}x_ix_j , where a_{ij}=a_{ji} \in Z.
Revised: An n-ary integral quadratic form is a homogeneous polynomial of uniform degree~2 in several variables e.g., an n-ary integral quadratic form in variables x_1, \cdots ,x_n looks like \sum _{1\leq i,j\leq n}a_{ij}x_ix_j , where a_{ij}=a_{ji} \in Z.
Edit intent: fluency
Original: An  integral quadratic form is a homogeneous polynomial of uniform degree~2 in several variables e.g., an n-ary integral quadratic form in variables x_1, \cdots ,x_n looks like \sum _{1\leq i,j\leq n}a_{ij}x_ix_j , where a_{ij}=a_{ji} \in Z.
Revised: An integral quadratic form is a homogeneous polynomial of uniform degree~2 in several variables e.g., an n-ary integral quadratic form in variables x_1, ... ,x_n looks like \sum _{1\leq i,j\leq n}a_{ij}x_ix_j , where a_{ij}=a_{ji} \in Z.
Edit intent: clarity
Original: An  integral quadratic form is a homogeneous polynomial of uniform degree~2 in several variables e.g., an n-ary integral quadratic form in variables x_1, \cdots ,x_n looks like \sum _{1\leq i,j\leq n}a_{ij}x_ix_j , where a_{ij}=a_{ji} \in Z.
Revised: An integral quadratic form is a homogeneous polynomial of uniform degree~2 in several variables e.g., an n-ary integral quadratic form in variables x_1, \cdots ,x_n )=\sum _{1\leq i,j\leq n}a_{ij}x_ix_j , where a_{ij}=a_{ji} \in Z.
Edit intent: coherence
Original:  We present a \text{poly (n,k, \log p, \log t) randomize algorithm that given a quadratic form \mathtt{Q and an integer t, samples a uniform solution of \mathtt{Q (x_1, \cdots ,x_n)\equiv t \bmod{p^k}.
Revised:  We present a poly (n,k, \log p, \log t) randomize algorithm that given a quadratic form \mathtt{Q and an integer t, samples a uniform solution of \mathtt{Q (x_1, \cdots ,x_n)\equiv t \bmod{p^k}.
Edit intent: fluency
Original:  We present a \text{poly (n,k, \log p, \log t) randomize algorithm that given a quadratic form \mathtt{Q and an integer t, samples a uniform solution of \mathtt{Q (x_1, \cdots ,x_n)\equiv t \bmod{p^k}.
Revised:  We present a \text{poly (n,k, \log p, \log t) randomized algorithm that given a quadratic form \mathtt{Q and an integer t, samples a uniform solution of \mathtt{Q (x_1, \cdots ,x_n)\equiv t \bmod{p^k}.
Edit intent: fluency
Original:  We present a \text{poly (n,k, \log p, \log t) randomize algorithm that given a quadratic form \mathtt{Q and an integer t, samples a uniform solution of \mathtt{Q (x_1, \cdots ,x_n)\equiv t \bmod{p^k}.
Revised:  We present a \text{poly (n,k, \log p, \log t) randomize algorithm that given a quadratic form \mathtt{Q and an integer t, samples a uniform solution of Q (x_1, \cdots ,x_n)\equiv t \bmod{p^k}.
Edit intent: fluency
Original: This paper addresses the question of non-arbitrage (precisely No-Unbounded-Profit-with-Bounded-Risk , NUPBR hereafter) after a specific random time.
Revised: This paper addresses the question of non-arbitrage notion of No-Unbounded-Profit-with-Bounded-Risk , NUPBR hereafter) after a specific random time.
Edit intent: clarity
Original: This paper addresses the question of non-arbitrage (precisely No-Unbounded-Profit-with-Bounded-Risk , NUPBR hereafter) after a specific random time.
Revised: This paper addresses the question of non-arbitrage (precisely No-Unbounded-Profit-with-Bounded-Risk ( NUPBR hereafter) after a specific random time.
Edit intent: fluency
Original: This paper addresses the question of non-arbitrage (precisely No-Unbounded-Profit-with-Bounded-Risk , NUPBR hereafter) after a specific random time.
Revised: This paper addresses the question of non-arbitrage (precisely No-Unbounded-Profit-with-Bounded-Risk , NUPBR hereafter) and additional information generated by a random time.
Edit intent: clarity
Original:  This study completes the one of Aksamit et al.
Revised:  This study complements the one of Aksamit et al.
Edit intent: fluency
Original: The current biochemical information processing systems behave in a pre-determined manner because all features are defined during the design phase.
Revised: The current biochemical information processing systems behave in a predetermined manner because all features are defined during the design phase.
Edit intent: fluency
Original:  In particular, we show that PSelInv can run efficient on more than 4,000 processors for a modestly sized matrix.
Revised:  In particular, we show that PSelInv can run efficiently on more than 4,000 processors for a modestly sized matrix.
Edit intent: fluency
Original:  In particular, we show that PSelInv can run efficiently on more than 4,000 processors for a modestly sized matrix.
Revised:  In particular, we show that PSelInv can run efficiently on more than 4,000 cores for a modestly sized matrix.
Edit intent: clarity
Original:  The encoding is demonstrated in a simple asymmetric concurrent pattern calculus before generalised to simplify infinite terms, and to show encodings into Concurrent Pattern Calculus and Psi calculus .
Revised:  The encoding is demonstrated in a simple asymmetric concurrent pattern calculus before generalised to simplify infinite terms, and to show encodings into Concurrent Pattern Calculus and Psi Calculi .
Edit intent: fluency
Original: HiRE-RNA is a simplified, coarse-grained model, developed in recent years to address the question of RNA folding for the prediction of equilibrium configurations, dynamics and thermodynamics.
Revised: HiRE-RNA is a simplified, coarse-grained RNA model for the prediction of equilibrium configurations, dynamics and thermodynamics.
Edit intent: clarity
Original: We study the complexity of computing Kronecker coefficients g(\lambda,\mu,\nu).
Revised: We study the complexity of computing Kronecker coefficients g(\lambda,\mu,\nu).
Edit intent: fluency
Original:  We give explicit bounds in terms of the number of parts ~ \ell in the partitions, their largest part size N and the smallest second part ~ M of the three partitions.
Revised:  We give explicit bounds in terms of the number of parts \ell in the partitions, their largest part size N and the smallest second part ~ M of the three partitions.
Edit intent: fluency
Original:  We give explicit bounds in terms of the number of parts ~ \ell in the partitions, their largest part size N and the smallest second part ~ M of the three partitions.
Revised:  We give explicit bounds in terms of the number of parts ~ \ell in the partitions, their largest part size N and the smallest second part M of the three partitions.
Edit intent: fluency
Original:  When M = O(1), i.e. ~ one of the partitions is ~hook-like , the bounds are linear in ~ \log N, but depend exponentially on ~ \ell.
Revised:  When M = O(1), i.e. one of the partitions is ~hook-like , the bounds are linear in ~ \log N, but depend exponentially on ~ \ell.
Edit intent: fluency
Original:  When M = O(1), i.e. ~ one of the partitions is ~hook-like , the bounds are linear in ~ \log N, but depend exponentially on ~ \ell.
Revised:  When M = O(1), i.e. ~ one of the partitions is hook-like , the bounds are linear in ~ \log N, but depend exponentially on ~ \ell.
Edit intent: fluency
Original:  When M = O(1), i.e. ~ one of the partitions is ~hook-like , the bounds are linear in ~ \log N, but depend exponentially on ~ \ell.
Revised:  When M = O(1), i.e. ~ one of the partitions is ~hook-like , the bounds are linear in ~ \log N, but depend exponentially on ~ \ell.
Edit intent: fluency
Original:  When M = O(1), i.e. ~ one of the partitions is ~hook-like , the bounds are linear in ~ \log N, but depend exponentially on ~ \ell.
Revised:  When M = O(1), i.e. ~ one of the partitions is ~hook-like , the bounds are linear in \log N, but depend exponentially on ~ \ell.
Edit intent: fluency
Original:  When M = O(1), i.e. ~ one of the partitions is ~hook-like , the bounds are linear in ~ \log N, but depend exponentially on ~ \ell.
Revised:  When M = O(1), i.e. ~ one of the partitions is ~hook-like , the bounds are linear in ~ \log N, but depend exponentially on \ell.
Edit intent: fluency
Original:  By a separate argument, we show that the positivity of Kronecker coefficients can be decided in O(\log N) time for a bounded number ~ \ell of parts and without restriction on ~ M. Related problems of computing Kronecker coefficients when one partition is a hook, and computing characters of ~ S_n are also considered.
Revised:  By a separate argument, we show that the positivity of Kronecker coefficients can be decided in O(\log N) time for a bounded number \ell of parts and without restriction on ~ M. Related problems of computing Kronecker coefficients when one partition is a hook, and computing characters of ~ S_n are also considered.
Edit intent: fluency
Original:  By a separate argument, we show that the positivity of Kronecker coefficients can be decided in O(\log N) time for a bounded number ~ \ell of parts and without restriction on ~ M. Related problems of computing Kronecker coefficients when one partition is a hook, and computing characters of ~ S_n are also considered.
Revised:  By a separate argument, we show that the positivity of Kronecker coefficients can be decided in O(\log N) time for a bounded number ~ \ell of parts and without restriction on M. Related problems of computing Kronecker coefficients when one partition is a hook, and computing characters of ~ S_n are also considered.
Edit intent: fluency
Original:  By a separate argument, we show that the positivity of Kronecker coefficients can be decided in O(\log N) time for a bounded number ~ \ell of parts and without restriction on ~ M. Related problems of computing Kronecker coefficients when one partition is a hook, and computing characters of ~ S_n are also considered.
Revised:  By a separate argument, we show that the positivity of Kronecker coefficients can be decided in O(\log N) time for a bounded number ~ \ell of parts and without restriction on ~ M. Related problems of computing Kronecker coefficients when one partition is a hook, and computing characters of S_n are also considered.
Edit intent: fluency
Original:  In particular, I argue that Stapp's model is circular , insofar as the mind/matter problem as concerned.
Revised:  In particular, I argue that Stapp's model is circular , insofar as the mind/matter problem is concerned.
Edit intent: fluency
Original: Topological constraints can affect both equilibrium and dynamics of polymer systems, and can play a role in chromosome organization in the cell.
Revised: Topological constraints can affect both equilibrium and dynamic properties of polymer systems, and can play a role in chromosome organization in the cell.
Edit intent: clarity
Original:   We prove that the decision tree complexity of 3SUM is O(n^{3/2}\log n) , that there is a randomized 3SUM algorithm running in O(n^2 (\log \log n)^2 /\log n) time, and a deterministic algorithm running in O(n^2 (\log\log n) ^{5/3 / ( \log n) ^{2/3) time .
Revised:  We prove that the decision tree complexity of 3SUM is O(n^{3/2}\log n) , that there is a randomized 3SUM algorithms, a deterministic one running in O(n^2 (\log \log n)^2 /\log n) time, and a deterministic algorithm running in O(n^2 (\log\log n) ^{5/3 / ( \log n) ^{2/3) time .
Edit intent: clarity
Original:   We prove that the decision tree complexity of 3SUM is O(n^{3/2}\log n) , that there is a randomized 3SUM algorithm running in O(n^2 (\log \log n)^2 /\log n) time, and a deterministic algorithm running in O(n^2 (\log\log n) ^{5/3 / ( \log n) ^{2/3) time .
Revised:  We prove that the decision tree complexity of 3SUM is O(n^{3/2}\log n) , that there is a randomized 3SUM algorithm running in O(n^2 / (\log n /\log n) time, and a deterministic algorithm running in O(n^2 (\log\log n) ^{5/3 / ( \log n) ^{2/3) time .
Edit intent: coherence
Original:   We prove that the decision tree complexity of 3SUM is O(n^{3/2}\log n) , that there is a randomized 3SUM algorithm running in O(n^2 (\log \log n)^2 /\log n) time, and a deterministic algorithm running in O(n^2 (\log\log n) ^{5/3 / ( \log n) ^{2/3) time .
Revised:  We prove that the decision tree complexity of 3SUM is O(n^{3/2}\log n) , that there is a randomized 3SUM algorithm running in O(n^2 (\log \log n)^2 /\log n) time, and a deterministic algorithm running in O(n^2 (\log\log n) ^{5/3 / \log n) ^{2/3) time .
Edit intent: coherence
Original:  }  Our results lead directly to improved algorithms for k-variate linear degeneracy testing for all odd k\ge 3.
Revised:  } Our results lead directly to improved bounds for k-variate linear degeneracy testing for all odd k\ge 3.
Edit intent: clarity
Original:  The problem is to decide, given a linear function f(x_1,\ldots,x_k) = \alpha_0 + 1\le i\le k \alpha_i x_i and a set S \subset \mathbb{R}, whether 0\in f( S ^k).
Revised:  The problem is to decide, given a linear function f(x_1,\ldots,x_k) = \alpha_0 + 1\le i\le k \alpha_i x_i and a set S \subset \mathbb{R}, whether 0\in f( A ^k).
Edit intent: clarity
Original:  We show the decision tree complexity  is O(n^{k/2}\sqrt{\log n}) and give algorithms running in time O(n^{(k+1)/2 / \mathrm{poly}(\log n))} . Finally, we give a subcubic algorithm for a generalization of the (\min,+)-product over real-valued matrices and apply it to the problem of finding zero-weight triangles in weighted graphs.
Revised:  We show the decision tree complexity is O(n^{k/2}\sqrt{\log n}) / \mathrm{poly}(\log n))} . Finally, we give a subcubic algorithm for a generalization of the (\min,+)-product over real-valued matrices and apply it to the problem of finding zero-weight triangles in weighted graphs.
Edit intent: clarity
Original:  A depth-O(n^{5/2}\sqrt{\log n}) decision tree is given for this problem, as well as an algorithm running in time O(n^3 (\log\log n)^2/\log n).
Revised:  We give a depth-O(n^{5/2}\sqrt{\log n}) decision tree is given for this problem, as well as an algorithm running in time O(n^3 (\log\log n)^2/\log n).
Edit intent: coherence
Original:  A depth-O(n^{5/2}\sqrt{\log n}) decision tree is given for this problem, as well as an algorithm running in time O(n^3 (\log\log n)^2/\log n).
Revised:  A depth-O(n^{5/2}\sqrt{\log n}) decision tree for this problem, as well as an algorithm running in time O(n^3 (\log\log n)^2/\log n).
Edit intent: clarity
Original:  We namely design a procedure working in 2^{O(k^5\log k)}\cdot n^5 time that, for a given graph G on n vertices, either concludes that the treewidth of G is at least k, or finds an isomorphism-invariant construction term - an algebraic expression that encodes G together with a tree decomposition of G of width O(k^4).
Revised:  We namely design a procedure working in 2^{O(k^5\log k)}\cdot n^5 time that, for a given graph G on n vertices, either concludes that the treewidth of G is at least k, or finds an isomorphism-invariant construction term --- an algebraic expression that encodes G together with a tree decomposition of G of width O(k^4).
Edit intent: fluency
Original:  Hence, a canonical graph isomorphic to G can be constructed by simply evaluating the obtained construction term, while the isomorphism test reduces to verifying whether the computed  construction terms for G_1 and G_2 are equal.
Revised:  Hence, the isomorphism test reduces to verifying whether the computed construction terms for G_1 and G_2 are equal.
Edit intent: coherence
Original:  I show that this new measure and existing measures of biodiversity change such as the Living Planet Index describe different aspects of dynamics , that can be thought of as "shape" and "size" change respectively .
Revised:  I show that this new measure and existing measures of biodiversity change such as the Living Planet Index describe different aspects of dynamics .
Edit intent: clarity
Original:  I show that neither environmental harshness, body size , nor environmental variability need affect the rate of "shape " change.
Revised:  I show that neither body size nor environmental variability need affect the rate of "shape " change.
Edit intent: clarity
Original:  I show that neither environmental harshness, body size , nor environmental variability need affect the rate of "shape " change.
Revised:  I show that neither environmental harshness, body size , nor environmental variability need affect the rate of shape change.
Edit intent: fluency
Original:  I extend the approach to deal with colonizations and extinctions, using the surreal number system.
Revised:  I extend the measure to deal with colonizations and extinctions, using the surreal number system.
Edit intent: clarity
Original:  I hypothesize that phylogenetically-restricted assemblages will show a higher proportion of "size " change than diverse communities.
Revised:  I hypothesize that phylogenetically-restricted assemblages will show a higher proportion of size change than diverse communities.
Edit intent: fluency
Original:  While a mathematical treatment of the costs and benefits of decisions can predict the optimal strategy in simple settings, more realistic situations ( finite populations, non-vanishing mutations rates,  communication between agents, and spatial interactions ) require agent-based methods where each agent is modeled as an individual, carries its own genes that determine its decisions, and where the evolutionary outcome can only be ascertained by evolving the population of agents forward in time.
Revised:  While a mathematical treatment of the costs and benefits of decisions can predict the optimal strategy in simple settings, more realistic settings such as finite populations, non-vanishing mutations rates, communication between agents, and spatial interactions ) require agent-based methods where each agent is modeled as an individual, carries its own genes that determine its decisions, and where the evolutionary outcome can only be ascertained by evolving the population of agents forward in time.
Edit intent: clarity
Original:  While a mathematical treatment of the costs and benefits of decisions can predict the optimal strategy in simple settings, more realistic situations ( finite populations, non-vanishing mutations rates,  communication between agents, and spatial interactions ) require agent-based methods where each agent is modeled as an individual, carries its own genes that determine its decisions, and where the evolutionary outcome can only be ascertained by evolving the population of agents forward in time.
Revised:  While a mathematical treatment of the costs and benefits of decisions can predict the optimal strategy in simple settings, more realistic situations ( finite populations, non-vanishing mutations rates, stochastic decisions, communication between agents, and spatial interactions ) require agent-based methods where each agent is modeled as an individual, carries its own genes that determine its decisions, and where the evolutionary outcome can only be ascertained by evolving the population of agents forward in time.
Edit intent: clarity