wanyu/IteraTeR_v2 huggingface dataset:
Original:  In this paper we propose an alternative approach , that relies on the expected profit maximization problem of an agent  producing and storing a commodity while trading in the associated futures contracts.
Revised:  In this article, we propose an alternative approach , that relies on the expected profit maximization problem of an agent producing and storing a commodity while trading in the associated futures contracts.
Edit intent: fluency
Original:  In this paper we propose an alternative approach , that relies on the expected profit maximization problem of an agent  producing and storing a commodity while trading in the associated futures contracts.
Revised:  In this paper we propose an alternative approach that relies on the expected profit maximization problem of an agent producing and storing a commodity while trading in the associated futures contracts.
Edit intent: fluency
Original:  In this paper we propose an alternative approach , that relies on the expected profit maximization problem of an agent  producing and storing a commodity while trading in the associated futures contracts.
Revised:  In this paper we propose an alternative approach , that relies on the expected profit maximization problem of an agent , producing and storing a commodity while trading in the associated futures contracts.
Edit intent: fluency
Original:  This approach is particularly interesting in the case of energy commodity: it remains suitable for commodities characterized by storability constraints, when standard no-arbitrage arguments can not be safely applied.
Revised:  This approach is particularly interesting in the case of energy commodity: it remains suitable for commodities characterized by storability constraints, when standard no-arbitrage arguments cannot be safely applied.
Edit intent: fluency
Original:  The objective is to find a path whose cost is at most (1+ \epsilon )OPT where OPT is the cost of an optimal path between s and t.
Revised:  The objective is to find a path whose cost is at most (1+ epsilon )OPT where OPT is the cost of an optimal path between s and t.
Edit intent: fluency
Original:  We define a new parameter for hypergraphs - " cover-independence number \gamma " and prove that \log \frac{|V|{\gamma} and |V|{2\gamma} } {\gamma(G)} and |V|{2\gamma(G)} } are lower bounds for \chi^c(G) and \chi(G), respectively.
Revised:  We define a new parameter for hypergraphs - " cover independence number \gamma(G) " and prove that \log \frac{|V|{\gamma} and |V|{2\gamma} } {\gamma(G)} and |V|{2\gamma(G)} } are lower bounds for \chi^c(G) and \chi(G), respectively.
Edit intent: clarity
Original:  We define a new parameter for hypergraphs - " cover-independence number \gamma " and prove that \log \frac{|V|{\gamma} and |V|{2\gamma} } {\gamma(G)} and |V|{2\gamma(G)} } are lower bounds for \chi^c(G) and \chi(G), respectively.
Revised:  We define a new parameter for hypergraphs - " cover-independence number \gamma " and prove that \log {\gamma} and |V|{2\gamma} } {\gamma(G)} and |V|{2\gamma(G)} } are lower bounds for \chi^c(G) and \chi(G), respectively.
Edit intent: clarity
Original:  We define a new parameter for hypergraphs - " cover-independence number \gamma " and prove that \log \frac{|V|{\gamma} and |V|{2\gamma} } {\gamma(G)} and |V|{2\gamma(G)} } are lower bounds for \chi^c(G) and \chi(G), respectively.
Revised:  We define a new parameter for hypergraphs - " cover-independence number \gamma " and prove that \log \frac{|V|{\gamma} and |V|{2\gamma} } \frac{|V|{\gamma(G)} and |V|{2\gamma(G)} } are lower bounds for \chi^c(G) and \chi(G), respectively.
Edit intent: fluency
Original:  We show that \chi^c(G) and \chi(G) can be approximated by polynomial time algorithms achieving approximation ratios \frac{1 , if \gamma(G)=n^t, where t<1.
Revised:  We show that \chi^c(G) can be approximated by polynomial time algorithms achieving approximation ratios \frac{1 , if \gamma(G)=n^t, where t<1.
Edit intent: clarity
Original:  We also construct a particular class of hypergraphs  called {\it cover-friendly } hypergraphs where the gap between \alpha(G) and \gamma(G) is arbitrarily large.
Revised:  We also construct a particular class of hypergraphs called {\it cover friendly } hypergraphs where the gap between \alpha(G) and \gamma(G) is arbitrarily large.
Edit intent: fluency
Original:  We also construct a particular class of hypergraphs  called {\it cover-friendly } hypergraphs where the gap between \alpha(G) and \gamma(G) is arbitrarily large.
Revised:  We also construct a particular class of hypergraphs called {\it cover-friendly } hypergraphs where the ratio of \alpha(G) and \gamma(G) is arbitrarily large.
Edit intent: clarity
Original:  We also construct a particular class of hypergraphs  called {\it cover-friendly } hypergraphs where the gap between \alpha(G) and \gamma(G) is arbitrarily large.
Revised:  We also construct a particular class of hypergraphs called {\it cover-friendly } hypergraphs where the gap between \alpha(G) to \gamma(G) is arbitrarily large.
Edit intent: fluency
Original:  We also construct a particular class of hypergraphs  called {\it cover-friendly } hypergraphs where the gap between \alpha(G) and \gamma(G) is arbitrarily large.
Revised:  We also construct a particular class of hypergraphs called {\it cover-friendly } hypergraphs where the gap between \alpha(G) and \gamma(G) can be arbitrarily large.
Edit intent: clarity
Original:  Let the {\it dependency d(G)} of G be the maximum number of neighbours of any hyperedge in G. We show using a Kolmogorov complexity argument that there is a bicoloring cover of size x for G if d(G) \leq 2^{x (k-1)-3 (\frac{2^{x(k-1)}}{e}-1) applying the local lemma for demonstrating a bicoloring cover of size x (\frac{2^{k-1}}{e}-1) using nx+kx\frac{m}{d} and n+2k\frac{m}{d} random bits, respectively} .
Revised:  Let the {\it dependency d(G)} of G be the maximum number of hyperedge neighbors of any hyperedge in G. We show using a Kolmogorov complexity argument that there is a bicoloring cover of size x for G if d(G) \leq 2^{x (k-1)-3 (\frac{2^{x(k-1)}}{e}-1) applying the local lemma for demonstrating a bicoloring cover of size x (\frac{2^{k-1}}{e}-1) using nx+kx\frac{m}{d} and n+2k\frac{m}{d} random bits, respectively} .
Edit intent: fluency
Original:  Let the {\it dependency d(G)} of G be the maximum number of neighbours of any hyperedge in G. We show using a Kolmogorov complexity argument that there is a bicoloring cover of size x for G if d(G) \leq 2^{x (k-1)-3 (\frac{2^{x(k-1)}}{e}-1) applying the local lemma for demonstrating a bicoloring cover of size x (\frac{2^{k-1}}{e}-1) using nx+kx\frac{m}{d} and n+2k\frac{m}{d} random bits, respectively} .
Revised:  Let the {\it dependency d(G)} of G be the maximum number of neighbours of any hyperedge in G. We propose algorithms for computing bicoloring cover of size x for G if d(G) \leq 2^{x (k-1)-3 (\frac{2^{x(k-1)}}{e}-1) applying the local lemma for demonstrating a bicoloring cover of size x (\frac{2^{k-1}}{e}-1) using nx+kx\frac{m}{d} and n+2k\frac{m}{d} random bits, respectively} .
Edit intent: clarity
Original:  Let the {\it dependency d(G)} of G be the maximum number of neighbours of any hyperedge in G. We show using a Kolmogorov complexity argument that there is a bicoloring cover of size x for G if d(G) \leq 2^{x (k-1)-3 (\frac{2^{x(k-1)}}{e}-1) applying the local lemma for demonstrating a bicoloring cover of size x (\frac{2^{k-1}}{e}-1) using nx+kx\frac{m}{d} and n+2k\frac{m}{d} random bits, respectively} .
Revised:  Let the {\it dependency d(G)} of G be the maximum number of neighbours of any hyperedge in G. We show using a Kolmogorov complexity argument that there is a bicoloring cover of size x for G if d(G) is at most (\frac{2^{x(k-1)}}{e}-1) applying the local lemma for demonstrating a bicoloring cover of size x (\frac{2^{k-1}}{e}-1) using nx+kx\frac{m}{d} and n+2k\frac{m}{d} random bits, respectively} .
Edit intent: clarity
Original: We prove that for any t\geq 1, there exists a k-uniform hypergraph G such that the {\it clique number} \omega(G)=k and \chi^c(G) > t. Let m( 2, k,x) denote the minimum number of hyperedges  such that some k-uniform hypergraph G with m( 2, k,x) hyperedges does not have a bicoloring cover of size x.
Revised: We prove that for any t\geq 1, there exists a k-uniform hypergraph G such that the {\it clique number} \omega(G)=k and \chi^c(G) > t. Let m( k,x) denote the minimum number of hyperedges such that some k-uniform hypergraph G with m( 2, k,x) hyperedges does not have a bicoloring cover of size x.
Edit intent: fluency
Original: We prove that for any t\geq 1, there exists a k-uniform hypergraph G such that the {\it clique number} \omega(G)=k and \chi^c(G) > t. Let m( 2, k,x) denote the minimum number of hyperedges  such that some k-uniform hypergraph G with m( 2, k,x) hyperedges does not have a bicoloring cover of size x.
Revised: We prove that for any t\geq 1, there exists a k-uniform hypergraph G such that the {\it clique number} \omega(G)=k and \chi^c(G) > t. Let m( 2, k,x) denote the minimum number of hyperedges such that some k-uniform hypergraph G with m( k,x) hyperedges does not have a bicoloring cover of size x.
Edit intent: fluency
Original:  Let the {\it dependency d(G)} of G be the maximum number of hyperedge neighbors of any hyperedge in G. We propose algorithms for computing bicoloring cover of size x for G if d(G) is at most (2^{x(k-1)}{e}-1) and 2^{x-1 using nx+kxm{d} and n+2k\frac{m .
Revised:  Let the {\it dependency d(G)} of G be the maximum number of hyperedge neighbors of any hyperedge in G. We propose an algorithm for computing a bicoloring cover of size x for G if d(G) is at most (2^{x(k-1)}{e}-1) and 2^{x-1 using nx+kxm{d} and n+2k\frac{m .
Edit intent: fluency
Original:  Let the {\it dependency d(G)} of G be the maximum number of hyperedge neighbors of any hyperedge in G. We propose algorithms for computing bicoloring cover of size x for G if d(G) is at most (2^{x(k-1)}{e}-1) and 2^{x-1 using nx+kxm{d} and n+2k\frac{m .
Revised:  Let the {\it dependency d(G)} of G be the maximum number of hyperedge neighbors of any hyperedge in G. We propose algorithms for computing bicoloring cover of size x for G if d(G) \leq (2^{x(k-1)}{e}-1) and 2^{x-1 using nx+kxm{d} and n+2k\frac{m .
Edit intent: clarity
Original:  Let the {\it dependency d(G)} of G be the maximum number of hyperedge neighbors of any hyperedge in G. We propose algorithms for computing bicoloring cover of size x for G if d(G) is at most (2^{x(k-1)}{e}-1) and 2^{x-1 using nx+kxm{d} and n+2k\frac{m .
Revised:  Let the {\it dependency d(G)} of G be the maximum number of hyperedge neighbors of any hyperedge in G. We propose algorithms for computing bicoloring cover of size x for G if d(G) is at most (2^{x(k-1)}{e}-1) using nx+kxm{d} and n+2k\frac{m .
Edit intent: fluency
Original:  We also consider two special cases of this problem: (i) We show, using a somewhat subtle construction, that if S consists of points on three lines, the number of unit-area triangles that S spans , with one vertex on each of the lines, can be \Omega(n^2), for any triple of lines ( this number is always O(n^2) in this case).
Revised:  We also consider two special cases of this problem: (i) We show, using a somewhat subtle construction, that if S consists of points on three lines, the number of unit-area triangles that S spans can be \Omega(n^2), for any triple of lines ( this number is always O(n^2) in this case).
Edit intent: clarity
Original:  We also consider two special cases of this problem: (i) We show, using a somewhat subtle construction, that if S consists of points on three lines, the number of unit-area triangles that S spans , with one vertex on each of the lines, can be \Omega(n^2), for any triple of lines ( this number is always O(n^2) in this case).
Revised:  We also consider two special cases of this problem: (i) We show, using a somewhat subtle construction, that if S consists of points on three lines, the number of unit-area triangles that S spans , with one vertex on each of the lines, can be \Omega(n^2), for any triple of lines ( it is always O(n^2) in this case).
Edit intent: clarity
Original:  Here we investigate the motile behavior of nematodes , which execute random walks driven by undulatory propulsion on surfaces .
Revised:  Here we investigate the motile behavior of nematodes at the level of their translational motion on surfaces driven by undulatory propulsion on surfaces .
Edit intent: clarity
Original:  Here we investigate the motile behavior of nematodes , which execute random walks driven by undulatory propulsion on surfaces .
Revised:  Here we investigate the motile behavior of nematodes , which execute random walks driven by undulatory propulsion .
Edit intent: clarity
Original:  We broadly sample the nematode behavioral repertoire by measuring motile trajectories of the canonical lab strain C. elegans N2 , wild strains and distant species.
Revised:  We broadly sample the nematode behavioral repertoire by measuring motile trajectories of the canonical lab strain C. elegans N2 , wild strains and distant species.
Edit intent: fluency
Original:  We broadly sample the nematode behavioral repertoire by measuring motile trajectories of the canonical lab strain C. elegans N2 , wild strains and distant species.
Revised:  We broadly sample the nematode behavioral repertoire by measuring motile trajectories of the canonical lab strain C. elegans N2 as well as wild strains and distant species.
Edit intent: clarity
Original:  We focus on trajectory dynamics over timescales spanning the transition from ballistic to diffusive movement and find that much of the statistics of nematode exploratory behavior are captured by a random walk model with independent dynamics in the speed and bearing.
Revised:  We focus on trajectory dynamics over timescales spanning the transition from ballistic to diffusive movement and find that salient features of the motility statistics are captured by a random walk model with independent dynamics in the speed and bearing.
Edit intent: clarity
Original:  Furthermore, the parameters describing this behavioral model vary among individuals and across species in a correlated way that suggests a common mode of behavioral control and is consistent with a trade-off between exploratory and exploitative behavior .
Revised:  We show that the model parameters vary among species in a correlated way that suggests a common mode of behavioral control and is consistent with a trade-off between exploratory and exploitative behavior .
Edit intent: clarity
Original:  Furthermore, the parameters describing this behavioral model vary among individuals and across species in a correlated way that suggests a common mode of behavioral control and is consistent with a trade-off between exploratory and exploitative behavior .
Revised:  Furthermore, the parameters describing this behavioral model vary among individuals and across species in a correlated way that suggests a common mode of behavioral control and a trade-off between exploratory and exploitative behavior .
Edit intent: coherence
Original:  We broadly sample the nematode behavioral repertoire by measuring motile trajectories of the canonical lab strain C. elegans N2 as well as wild strains and distant species.
Revised:  We broadly sample the nematode behavioral repertoire by measuring motile trajectories of the canonical lab strain C. elegans N2 as well as wild strains and distant species.
Edit intent: fluency
Original:  We focus on trajectory dynamics over timescales spanning the transition from ballistic to diffusive movement and find that salient features of the motility statistics are captured by a random walk model with independent dynamics in the speed and bearing .
Revised:  We focus on trajectory dynamics over timescales spanning the transition from ballistic to diffusive movement and find that salient features of the motility statistics are captured by a random walk model with independent dynamics in the speed , bearing and reversal events .
Edit intent: clarity
Original:  The distribution of phenotypes along this primary mode of variation reveals that not only the mean but also the variance varies considerably across strains, suggesting that these clonal populations employ contrasting ' bet-hedging ' strategies for foraging.
Revised:  The distribution of phenotypes along this primary mode of variation reveals that not only the mean but also the variance varies considerably across strains, suggesting that these nematode lineages employ contrasting `` bet-hedging ' strategies for foraging.
Edit intent: clarity
Original:  The distribution of phenotypes along this primary mode of variation reveals that not only the mean but also the variance varies considerably across strains, suggesting that these clonal populations employ contrasting ' bet-hedging ' strategies for foraging.
Revised:  The distribution of phenotypes along this primary mode of variation reveals that not only the mean but also the variance varies considerably across strains, suggesting that these clonal populations employ contrasting ' bet-hedging '' strategies for foraging.
Edit intent: fluency
Original: We propose a generalized stochastic blockmodel to explore the mesoscopic structures in signed networks by grouping vertices that exhibit similar positive and negative connection profiles into the same cluster.
Revised: We propose a generalized stochastic block model to explore the mesoscopic structures in signed networks by grouping vertices that exhibit similar positive and negative connection profiles into the same cluster.
Edit intent: fluency
Original:  In this model, the group memberships are viewed as hidden or unobserved quantities  and the connection patterns between groups are explicitly characterized by two block matrices, one for the positive links and the other for negative ones .
Revised:  In this model, the group memberships are viewed as hidden or unobserved quantities , and the connection patterns between groups are explicitly characterized by two block matrices, one for the positive links and the other for negative ones .
Edit intent: fluency
Original:  In this model, the group memberships are viewed as hidden or unobserved quantities  and the connection patterns between groups are explicitly characterized by two block matrices, one for the positive links and the other for negative ones .
Revised:  In this model, the group memberships are viewed as hidden or unobserved quantities and the connection patterns between groups are explicitly characterized by two block matrices, one for positive links and the other for negative ones .
Edit intent: fluency
Original:  In this model, the group memberships are viewed as hidden or unobserved quantities  and the connection patterns between groups are explicitly characterized by two block matrices, one for the positive links and the other for negative ones .
Revised:  In this model, the group memberships are viewed as hidden or unobserved quantities and the connection patterns between groups are explicitly characterized by two block matrices, one for the positive links and the other for negative links .
Edit intent: clarity
Original:  As a by-product , the model parameters provide vital clues about the centrality of each vertex in its corresponding group and the probabilities that each vertex belongs to different groups  .
Revised:  Furthermore , the model parameters provide vital clues about the centrality of each vertex in its corresponding group and the probabilities that each vertex belongs to different groups .
Edit intent: coherence
Original:  As a by-product , the model parameters provide vital clues about the centrality of each vertex in its corresponding group and the probabilities that each vertex belongs to different groups  .
Revised:  As a by-product , the model parameters provide vital clues about the probabilities that each vertex belongs to different groups .
Edit intent: clarity
Original:  It implies that it is impossible to have a fully polynomial-time approximation scheme (FPTAS) for a large class of regularization problems unless P = NP  .
Revised:  It implies that it is impossible to have a fully polynomial-time approximation scheme (FPTAS) for such problems unless P = NP .
Edit intent: clarity
Original:  Moreover, for various brain regions such as the primary visual cortex, the system is bias toward some states over other states and, when representing this bias using a probability distribution , the system can define expected quantities.
Revised:  Moreover, for various brain regions such as the visual cortex, the system is bias toward some states over other states and, when representing this bias using a probability distribution , the system can define expected quantities.
Edit intent: clarity
Original:  Moreover, for various brain regions such as the primary visual cortex, the system is bias toward some states over other states and, when representing this bias using a probability distribution , the system can define expected quantities.
Revised:  Moreover, for various brain regions such as the primary visual cortex, the system is biased toward some states over other states and, when representing this bias using a probability distribution , the system can define expected quantities.
Edit intent: fluency
Original:  Moreover, for various brain regions such as the primary visual cortex, the system is bias toward some states over other states and, when representing this bias using a probability distribution , the system can define expected quantities.
Revised:  Moreover, for various brain regions such as the primary visual cortex, the system is bias toward some states . Representing this bias using a probability distribution , the system can define expected quantities.
Edit intent: coherence
Original:  Moreover, for various brain regions such as the primary visual cortex, the system is bias toward some states over other states and, when representing this bias using a probability distribution , the system can define expected quantities.
Revised:  Moreover, for various brain regions such as the primary visual cortex, the system is bias toward some states over other states and, when representing this bias using a probability distribution shows that the system can define expected quantities.
Edit intent: clarity
Original:  Under the requirement of minimising expected float entropy , the brain defines relationships.
Revised:  Under the requirement that the relationship parameters minimise efe , the brain defines relationships.
Edit intent: clarity
Original:  It is proposed that when a brain state is interpreted in the context of all these relationships the brain state acquires meaning in the form of the relational content of the associated experience.
Revised:  It is proposed that when a brain state is interpreted in the context of these relationships the brain state acquires meaning in the form of the relational content of the associated experience.
Edit intent: clarity
Original:  Empirical data indicates simple power-law scalings for the size distribution of cities (known as Zipf's law) , the geographic distribution of friends, and the population density fluctuations as a function of scale.
Revised:  Empirical data indicates simple power-law scalings for the size distribution of cities (known as Zipf's law) and the population density fluctuations as a function of scale.
Edit intent: clarity
Original:  The model enables the analytic computation of many new predictions for the spread of diseases and other social phenomena on highly spatially inhomogeneous populations by importing the mathematical formalism of random fields instead of traditional discrete graph techniques .
Revised:  The model enables the analytic computation of many new predictions by importing the mathematical formalism of random fields instead of traditional discrete graph techniques .
Edit intent: clarity