wanyu/IteraTeR_v2 huggingface dataset:
Original:  It may be noted that , for a general 1-connected graph G, rc(G) can be arbitrarily larger than its radius ( K_{1,n for instance).
Revised:  It may be noted that for a general 1-connected graph G, rc(G) can be arbitrarily larger than its radius ( K_{1,n for instance).
Edit intent: fluency
Original: Statistical properties of  double-auction markets with Bid-Ask spread in market order are investigated through the  response function.
Revised: Statistical properties of order-driven double-auction markets with Bid-Ask spread in market order are investigated through the response function.
Edit intent: clarity
Original: Statistical properties of  double-auction markets with Bid-Ask spread in market order are investigated through the  response function.
Revised: Statistical properties of double-auction markets with Bid-Ask spread are investigated through the response function.
Edit intent: clarity
Original:  We find that the MRR theory apparently fails to simulate so much as the qualitative behaviour ( ` non-monotonic' behaviour) of the response function  calculated from the data.
Revised:  We find that the MRR theory apparently fails to simulate so much as the qualitative behaviour ( ' non-monotonic' behaviour) of the response function calculated from the data.
Edit intent: fluency
Original:  Our main technical contributions are representation theorems showing that comtrace quotient monoid, combined dependency graph (Kleijn and Koutny 2008) and our labeled stratified order structure characterization are three different and yet equivalent ways to represent comtraces.
Revised:  Our main technical contributions are representation theorems showing that comtrace quotient monoid, combined dependency graph (Kleijn and Koutny 2008) and our labeled stratified order structure characterization are three different and yet equivalent ways to represent comtraces.
Edit intent: fluency
Original:  They also showed that comtraces corresponds to some class of labeled stratified order structures, but the question " what class of labeled stratified orders represent comtraces?" was left open .
Revised:  They also showed that comtraces correspond to some class of labeled stratified order structures, but the question " what class of labeled stratified orders represent comtraces?" was left open .
Edit intent: fluency
Original:  They also showed that comtraces corresponds to some class of labeled stratified order structures, but the question " what class of labeled stratified orders represent comtraces?" was left open .
Revised:  They also showed that comtraces corresponds to some class of labeled stratified order structures, but left open the question of what class of labeled stratified orders represent comtraces?" was left open .
Edit intent: fluency
Original:  They also showed that comtraces corresponds to some class of labeled stratified order structures, but the question " what class of labeled stratified orders represent comtraces?" was left open .
Revised:  They also showed that comtraces corresponds to some class of labeled stratified order structures, but the question " what class of labeled stratified orders represents comtraces .
Edit intent: clarity
Original: Combined traces (i.e., comtraces) , a generalization of Mazurkiewicz traces, were introduced by Janicki and Koutny in 1995 as  congruence classes of step sequences, where the congruence relation is induced by two relations simultaneity and serializability on events.
Revised: The combined trace (i.e., comtraces) , a generalization of Mazurkiewicz traces, were introduced by Janicki and Koutny in 1995 as congruence classes of step sequences, where the congruence relation is induced by two relations simultaneity and serializability on events.
Edit intent: clarity
Original: Combined traces (i.e., comtraces) , a generalization of Mazurkiewicz traces, were introduced by Janicki and Koutny in 1995 as  congruence classes of step sequences, where the congruence relation is induced by two relations simultaneity and serializability on events.
Revised: Combined traces (i.e., comtrace) notion was introduced by Janicki and Koutny in 1995 as congruence classes of step sequences, where the congruence relation is induced by two relations simultaneity and serializability on events.
Edit intent: clarity
Original: Combined traces (i.e., comtraces) , a generalization of Mazurkiewicz traces, were introduced by Janicki and Koutny in 1995 as  congruence classes of step sequences, where the congruence relation is induced by two relations simultaneity and serializability on events.
Revised: Combined traces (i.e., comtraces) , a generalization of Mazurkiewicz traces, were introduced by Janicki and Koutny in 1995 as a generalization of the Mazurkiewicz trace notion. Comtraces are congruence classes of step sequences, where the congruence relation is induced by two relations simultaneity and serializability on events.
Edit intent: clarity
Original: Combined traces (i.e., comtraces) , a generalization of Mazurkiewicz traces, were introduced by Janicki and Koutny in 1995 as  congruence classes of step sequences, where the congruence relation is induced by two relations simultaneity and serializability on events.
Revised: Combined traces (i.e., comtraces) , a generalization of Mazurkiewicz traces, were introduced by Janicki and Koutny in 1995 as congruence classes of step sequences, where the congruence relation is defined from two relations simultaneity and serializability on events.
Edit intent: clarity
Original: We study the optimal usage-based pricing problem in a resource-constrained network with one profit-maximizing Service Provider (SP) and multiple groups of surplus-maximizing users.
Revised: We study the optimal usage-based pricing problem in a resource-constrained network with one profit-maximizing service provider and multiple groups of surplus-maximizing users.
Edit intent: clarity
Original:  With the assumption that the SP knows the utility function of each user (thus complete information), we find that the complete price differentiation scheme can achieve a large revenue gain (e.g., 50\%) compared to no price differentiation, when the total network resource is comparably limited and the high willingness to pay users are minorities.
Revised:  With the assumption that the service provider knows the utility function of each user (thus complete information), we find that the complete price differentiation scheme can achieve a large revenue gain (e.g., 50\%) compared to no price differentiation, when the total network resource is comparably limited and the high willingness to pay users are minorities.
Edit intent: clarity
Original:  We also consider the incomplete information case where the SP does not know which group each user belongs to.
Revised:  We also consider the incomplete information case where the service provider does not know which group each user belongs to.
Edit intent: clarity
Original: In STOC'05, Indyk and Woodruff introduced a new technique that yielded a near-optimal space algorithm for F_k moment estimation problem.
Revised: A technique introduced by Indyk and Woodruff introduced a new technique that yielded a near-optimal space algorithm for F_k moment estimation problem.
Edit intent: clarity
Original:  We show that at least several of these results follow easily from the application of a single probabilistic technique, called Precision Sampling.
Revised:  We show that a number of these results follow easily from the application of a single probabilistic technique, called Precision Sampling.
Edit intent: clarity
Original:  We show that at least several of these results follow easily from the application of a single probabilistic technique, called Precision Sampling.
Revised:  We show that at least several of these results follow easily from the application of a single probabilistic method called Precision Sampling.
Edit intent: clarity
Original:  Using it , we obtain simple streaming algorithms that maintain a randomized sketch of an input vector x=(x_1,... , x_n),  useful for the following applications : Estimating the F_k moment of x, for k>2.
Revised:  Using this method , we obtain simple streaming algorithms that maintain a randomized sketch of an input vector x=(x_1,... , x_n), useful for the following applications : Estimating the F_k moment of x, for k>2.
Edit intent: clarity
Original:  Using it , we obtain simple streaming algorithms that maintain a randomized sketch of an input vector x=(x_1,... , x_n),  useful for the following applications : Estimating the F_k moment of x, for k>2.
Revised:  Using it , we obtain simple data-stream algorithms that maintain a randomized sketch of an input vector x=(x_1,... , x_n), useful for the following applications : Estimating the F_k moment of x, for k>2.
Edit intent: clarity
Original:  Using it , we obtain simple streaming algorithms that maintain a randomized sketch of an input vector x=(x_1,... , x_n),  useful for the following applications : Estimating the F_k moment of x, for k>2.
Revised:  Using it , we obtain simple streaming algorithms that maintain a randomized sketch of an input vector x=(x_1,... x_n), useful for the following applications : Estimating the F_k moment of x, for k>2.
Edit intent: fluency
Original:  Using it , we obtain simple streaming algorithms that maintain a randomized sketch of an input vector x=(x_1,... , x_n),  useful for the following applications : Estimating the F_k moment of x, for k>2.
Revised:  Using it , we obtain simple streaming algorithms that maintain a randomized sketch of an input vector x=(x_1,... , x_n), which is useful for the following applications : Estimating the F_k moment of x, for k>2.
Edit intent: coherence
Original:  Using it , we obtain simple streaming algorithms that maintain a randomized sketch of an input vector x=(x_1,... , x_n),  useful for the following applications : Estimating the F_k moment of x, for k>2.
Revised:  Using it , we obtain simple streaming algorithms that maintain a randomized sketch of an input vector x=(x_1,... , x_n), useful for the following applications . 1) Estimating the F_k moment of x, for k>2.
Edit intent: coherence
Original:  Using it , we obtain simple streaming algorithms that maintain a randomized sketch of an input vector x=(x_1,... , x_n),  useful for the following applications : Estimating the F_k moment of x, for k>2.
Revised:  Using it , we obtain simple streaming algorithms that maintain a randomized sketch of an input vector x=(x_1,... , x_n), useful for the following applications : Estimating the F_k -moment of x, for k>2.
Edit intent: clarity
Original:   Estimating the \ell_p norm of x, for p\in[1,2], with small update time.
Revised:  2) Estimating the \ell_p norm of x, for p\in[1,2], with small update time.
Edit intent: fluency
Original:   Estimating cascaded norms \ell_p(\ell_q) for all p,q>0.  \ell_1 sampling, where the goal is to produce an element i with probability (approximately) |x_i|/\|x\|_1.
Revised:  3) Estimating cascaded norms \ell_p(\ell_q) for all p,q>0. \ell_1 sampling, where the goal is to produce an element i with probability (approximately) |x_i|/\|x\|_1.
Edit intent: fluency
Original:  For all these applications the algorithm is essentially the same: topre-multiply the vector x entry-wise by a well-chosen random vector, and run a heavy hitter estimation algorithm on the resulting vector.
Revised:  For all these applications the algorithm is essentially the same: scale the vector x entry-wise by a well-chosen random vector, and run a heavy hitter estimation algorithm on the resulting vector.
Edit intent: clarity
Original:  For all these applications the algorithm is essentially the same: topre-multiply the vector x entry-wise by a well-chosen random vector, and run a heavy hitter estimation algorithm on the resulting vector.
Revised:  For all these applications the algorithm is essentially the same: topre-multiply the vector x entry-wise by a well-chosen random vector, and run a heavy-hitter estimation algorithm on the resulting vector.
Edit intent: fluency
Original:  More precisely, one chooses in advance ``precisions'' w_i%DIFDELCMD < \ge %%%  1 ] for each i\in[n] and obtains an estimate of  a_i within additive 1/w_i.
Revised:  More precisely, %DIFDELCMD < \ge %%% 1 ] for each i\in[n] and obtains an estimate of a_i within additive 1/w_i.
Edit intent: clarity
Original:  More precisely, one chooses in advance ``precisions'' w_i%DIFDELCMD < \ge %%%  1 ] for each i\in[n] and obtains an estimate of  a_i within additive 1/w_i.
Revised:  More precisely, one chooses in advance ``precisions'' w_i%DIFDELCMD < \ge %%% 1 ] for each i\in[n] , and then it receives an estimate of a_i within additive 1/w_i.
Edit intent: clarity
Original:  More precisely, one chooses in advance ``precisions'' w_i%DIFDELCMD < \ge %%%  1 ] for each i\in[n] and obtains an estimate of  a_i within additive 1/w_i.
Revised:  More precisely, one chooses in advance ``precisions'' w_i%DIFDELCMD < \ge %%% 1 ] for each i\in[n] and obtains an estimate of every a_i within additive 1/w_i.
Edit intent: clarity
Original:  In previous work , we showed [Andoni, Krauthgamer, and Onak, FOCS 2010] that, as long as \sum a_i=\Omega(1), one can achieve good multiplicative approximation  using total precision of only O(n\log n).
Revised:  In previous work , we showed [Andoni, Krauthgamer, and Onak, FOCS 2010] which shows that as long as \sum a_i=\Omega(1), one can achieve good multiplicative approximation using total precision of only O(n\log n).
Edit intent: coherence
Original:  In previous work , we showed [Andoni, Krauthgamer, and Onak, FOCS 2010] that, as long as \sum a_i=\Omega(1), one can achieve good multiplicative approximation  using total precision of only O(n\log n).
Revised:  In previous work , we showed [Andoni, Krauthgamer, and Onak, FOCS 2010] that, as long as \sum a_i=\Omega(1), a good multiplicative approximation using total precision of only O(n\log n).
Edit intent: clarity
Original: Much effort is spent everyday by programmers  trying to reduce long, failing execution traces to the cause of the error.
Revised: Much effort is spent everyday by programmers in trying to reduce long, failing execution traces to the cause of the error.
Edit intent: fluency
Original:  We present a new algorithm for error cause localization based on a reduction to the maximal satisfiability problem ( MAX SAT ), which asks what is the maximum number of clauses of a Boolean formula that can be  satisfied by an assignment.
Revised:  We present a new algorithm for error cause localization based on a reduction to the maximal satisfiability problem ( MAX-SAT ), which asks what is the maximum number of clauses of a Boolean formula that can be satisfied by an assignment.
Edit intent: clarity
Original:  We present a new algorithm for error cause localization based on a reduction to the maximal satisfiability problem ( MAX SAT ), which asks what is the maximum number of clauses of a Boolean formula that can be  satisfied by an assignment.
Revised:  We present a new algorithm for error cause localization based on a reduction to the maximal satisfiability problem ( MAX SAT ), which asks what is the maximum number of clauses of a Boolean formula that can be simultaneously satisfied by an assignment.
Edit intent: clarity
Original:  First, as in symbolic execution, we encode a trace of a program as a Boolean trace formula which is satisfiable iff the trace is feasible.
Revised:  First, using symbolic execution, we encode a trace of a program as a Boolean trace formula which is satisfiable iff the trace is feasible.
Edit intent: coherence
Original:  Second, for a failing program execution (e.g., one that violates an assertion or a post condition ), we construct an unsatisfiable formula by taking the trace formula and additionally asserting that the input is the failing test and that the post-condition holds .
Revised:  Second, for a failing program execution (e.g., one that violates an assertion or a post-condition ), we construct an unsatisfiable formula by taking the trace formula and additionally asserting that the input is the failing test and that the post-condition holds .
Edit intent: fluency
Original:  We have implemented our algorithm in a tool called Bug- Assist for C programs.
Revised:  We have implemented our algorithm in a tool called bug-assist for C programs.
Edit intent: fluency
Original:  We demonstrate the surprising effectiveness of Bug-Assist on a set of benchmark examples with injected faults, and show that in most cases, Bug-Assist can quickly and precisely isolate the exact few lines of code whose change eliminates the error.
Revised:  We demonstrate the surprising effectiveness of the tool on a set of benchmark examples with injected faults, and show that in most cases, Bug-Assist can quickly and precisely isolate the exact few lines of code whose change eliminates the error.
Edit intent: clarity
Original:  We demonstrate the surprising effectiveness of Bug-Assist on a set of benchmark examples with injected faults, and show that in most cases, Bug-Assist can quickly and precisely isolate the exact few lines of code whose change eliminates the error.
Revised:  We demonstrate the surprising effectiveness of Bug-Assist on a set of benchmark examples with injected faults, and show that in most cases, bug-assist can quickly and precisely isolate the exact few lines of code whose change eliminates the error.
Edit intent: fluency
Original: Given a set of alternatives to be ranked  and some pairwise comparison values, ranking can be posed as a least squares computation on a graph.
Revised: Given a set of alternatives to be ranked , and some pairwise comparison values, ranking can be posed as a least squares computation on a graph.
Edit intent: fluency
Original: Given a set of alternatives to be ranked  and some pairwise comparison values, ranking can be posed as a least squares computation on a graph.
Revised: Given a set of alternatives to be ranked and some pairwise comparison data, ranking is a least squares computation on a graph.
Edit intent: clarity
Original:  When \beta is a (-\beta)-number, which is the analogue of a Parry number, we describe their structure by a fixed point of an anti-morphism.
Revised:  When \beta is the analogue of a Parry number, we describe their structure by a fixed point of an anti-morphism.
Edit intent: coherence
Original: Can (scientific) knowledge be reliably preserved over the long term .
Revised: Can (scientific) knowledge be reliably preserved over the long term ?
Edit intent: fluency
Original:  But does this guarantee -- or does it even seem likely -- that all knowledge can be preserved over tens of thousands of years and beyond?
Revised:  But does this guarantee -- or does it even seem likely -- that all knowledge can be preserved over thousands of years and beyond?
Edit intent: clarity
Original:  The core of this algorithm is  decomposition theorem, which is used to deal with simplicial subdivision of T^{-}=\{y\in m| \beta^Ty\leq 0\} on  standard simplex \Delta_m, where each component of the vector \beta ^T is either -1 or 0 or 1.
Revised:  The core of this algorithm is a decomposition theorem, which is used to deal with simplicial subdivision of T^{-}=\{y\in m| \beta^Ty\leq 0\} on standard simplex \Delta_m, where each component of the vector \beta ^T is either -1 or 0 or 1.
Edit intent: fluency
Original:  The core of this algorithm is  decomposition theorem, which is used to deal with simplicial subdivision of T^{-}=\{y\in m| \beta^Ty\leq 0\} on  standard simplex \Delta_m, where each component of the vector \beta ^T is either -1 or 0 or 1.
Revised:  The core of this algorithm is decomposition theorem, which is used to deal with simplicial subdivision of T^{-}=\{y\in m| \beta^Ty\leq 0\} on the standard simplex \Delta_m, where each component of the vector \beta ^T is either -1 or 0 or 1.
Edit intent: fluency
Original:  The core of this algorithm is  decomposition theorem, which is used to deal with simplicial subdivision of T^{-}=\{y\in m| \beta^Ty\leq 0\} on  standard simplex \Delta_m, where each component of the vector \beta ^T is either -1 or 0 or 1.
Revised:  The core of this algorithm is decomposition theorem, which is used to deal with simplicial subdivision of T^{-}=\{y\in m| \beta^Ty\leq 0\} on standard simplex \Delta_m, where each component of the vector \beta is -1 or 0 or 1.
Edit intent: clarity
Original:  The core of this algorithm is  decomposition theorem, which is used to deal with simplicial subdivision of T^{-}=\{y\in m| \beta^Ty\leq 0\} on  standard simplex \Delta_m, where each component of the vector \beta ^T is either -1 or 0 or 1.
Revised:  The core of this algorithm is decomposition theorem, which is used to deal with simplicial subdivision of T^{-}=\{y\in m| \beta^Ty\leq 0\} on standard simplex \Delta_m, where each component of the vector \beta ^T is either -1 , 0 or 1.
Edit intent: fluency
Original: In this paper we propose a new design of LT codes, which decreases the average amount of redundancy in comparison to existing designs.
Revised: In this paper we propose a new design of LT codes, which decreases the amount of necessary overhead in comparison to existing designs.
Edit intent: clarity
Original:  In this work we argue that the ripple size should decrease during decoding, in order to reduce the redundancy .
Revised:  In this work we show that the ripple size should decrease during decoding, in order to reduce the redundancy .
Edit intent: clarity
Original:  In this work we argue that the ripple size should decrease during decoding, in order to reduce the redundancy .
Revised:  In this work we argue that the ripple size should decrease during decoding, in order to reduce the necessary overhead .
Edit intent: clarity
Original:  We then propose a new degree distribution, which provides the desired decreasing ripple size.
Revised:  We then propose a new design procedure, which can provide any desired achievable decreasing ripple size.
Edit intent: clarity
Original:  The new degree distribution is evaluated and compared to the current state of the art through simulations.
Revised:  The new design procedure is evaluated and compared to the current state of the art through simulations.
Edit intent: clarity
Original:  This reveals a noticeable increase in performance with respect to the average amount of redundancy .
Revised:  This reveals a significant increase in performance with respect to the average amount of redundancy .
Edit intent: clarity
Original:  This reveals a noticeable increase in performance with respect to the average amount of redundancy .
Revised:  This reveals a noticeable increase in performance with respect to both average overhead and error probability at any fixed overhead .
Edit intent: clarity
Original:  The algorithm is implementable to the Computer Algebra System(CAS) such as MAPLE, MATLAB and EMATICA .
Revised:  The algorithm is implementable to the Computer Algebra System(CAS) such as MAPLE, Matlab and Mathematica .
Edit intent: clarity
Original:  Using this analysis, we quantify the robustness of WCL to various physical conditions and provide  guidelines, such as node placement, for  practical deployment of WCL.
Revised:  Using this analysis, we quantify the robustness of WCL to various physical conditions and provide design guidelines, such as node placement, for practical deployment of WCL.
Edit intent: clarity
Original:  Using this analysis, we quantify the robustness of WCL to various physical conditions and provide  guidelines, such as node placement, for  practical deployment of WCL.
Revised:  Using this analysis, we quantify the robustness of WCL to various physical conditions and provide guidelines, such as node placement, for the practical deployment of WCL.
Edit intent: fluency
Original:  This approach achieves comparable accuracy with its centralized counterpart, and greatly reduces transmit power consumption .
Revised:  This approach achieves comparable accuracy with its centralized counterpart, and greatly reduces total transmit power .
Edit intent: clarity