wanyu/IteraTeR_v2 huggingface dataset:
Original:  These interpretations respectively help establish the structural centrality (C^{*}(i))  as a measure of both the overall position as well as the overall connectedness of node i in the network which in turn reflects the robustness of node i to random multiple edge failures.
Revised:  These interpretations respectively help establish the structural centrality (C^{*}(i)) as a measure of both the overall position as well as the overall connectedness of node i in the network ; thus reflecting the robustness of node i to random multiple edge failures.
Edit intent: coherence
Original:  Through empirical evaluations using synthetic and real world networks, we demonstrate how the structural centrality is better able to distinguish nodes in terms of their structural roles in the network and, along with Kirchoff index, is appropriately sensitive to perturbations/rewirings in the network.
Revised:  Through empirical evaluations using synthetic and real world networks, we demonstrate how the structural centrality is better able to distinguish nodes in terms of their structural roles in the network and, along with Kirchhoff index, is appropriately sensitive to perturbations/rewirings in the network.
Edit intent: fluency
Original:  In this paper we describe distributed algorithms for sampling networks, so that a node is selected with a probability that is a function of the distance of the node to a special node, called the source .
Revised:  In this paper we propose a distributed algorithm for sampling networks, so that a node is selected with a probability that is a function of the distance of the node to a special node, called the source .
Edit intent: clarity
Original:  In this paper we describe distributed algorithms for sampling networks, so that a node is selected with a probability that is a function of the distance of the node to a special node, called the source .
Revised:  In this paper we describe distributed algorithms for sampling networks, so that nodes are selected at a special node, called the source .
Edit intent: clarity
Original:  The basic technique used for sampling is a new class of random walks that start\emph{  at the source and always move  away from it , that we call Drifting Random Walks.
Revised:  The basic technique used for sampling is a new class of random walks , that we call\emph{ at the source and always move away from it , that we call Drifting Random Walks.
Edit intent: coherence
Original:  The basic technique used for sampling is a new class of random walks that start\emph{  at the source and always move  away from it , that we call Drifting Random Walks.
Revised:  The basic technique used for sampling is a new class of random walks that start\emph{ at the source and always away from it , that we call Drifting Random Walks.
Edit intent: clarity
Original:  The basic technique used for sampling is a new class of random walks that start\emph{  at the source and always move  away from it , that we call Drifting Random Walks.
Revised:  The basic technique used for sampling is a new class of random walks that start\emph{ at the source and always move moves away from it , that we call Drifting Random Walks.
Edit intent: clarity
Original:  At the end of the simulations, we have obtained that the average error of our sampling algorithm matches that of a centralized pseudorandom simulator .
Revised:  At the end of the simulations, we have obtained that the average error of our sampling algorithm matches that of a centralized pseudorandom simulatorexact probability distribution .
Edit intent: clarity
Original: Sampling a large network with a given probability distribution has been identified as a useful operation.
Revised: Sampling a network with a given probability distribution has been identified as a useful operation.
Edit intent: clarity
Original:  In this paper we propose a distributed algorithm for sampling networks, so that nodes are selected at a special node, called the source, with a given probability distribution.
Revised:  In this paper we propose distributed algorithms for sampling networks, so that nodes are selected at a special node, called the source, with a given probability distribution.
Edit intent: fluency
Original:  In this paper we propose a distributed algorithm for sampling networks, so that nodes are selected at a special node, called the source, with a given probability distribution.
Revised:  In this paper we propose a distributed algorithm for sampling networks, so that nodes are selected by a special node, called the source, with a given probability distribution.
Edit intent: clarity
Original:  This algorithm is based on a new class of random walks, that we call \emph{Drifting Random Walks (DRW ). A DRW starts at the source and always moves away from it.
Revised:  All these algorithms are based on a new class of random walks, that we call \emph{Drifting Random Walks (DRW ). A DRW starts at the source and always moves away from it.
Edit intent: coherence
Original:  This algorithm is based on a new class of random walks, that we call \emph{Drifting Random Walks (DRW ). A DRW starts at the source and always moves away from it.
Revised:  This algorithm is based on a new class of random walks, that we call \emph{ (DRW ). A DRW starts at the source and always moves away from it.
Edit intent: coherence
Original:  This algorithm is based on a new class of random walks, that we call \emph{Drifting Random Walks (DRW ). A DRW starts at the source and always moves away from it.
Revised:  This algorithm is based on a new class of random walks, that we call \emph{Drifting Random Walks (DRW ). A DRW starts at the source and always moves away from it.
Edit intent: fluency
Original:  A DRW algorithm has the novel key features that (1) it always finishes in a number of hops bounded by the network diameter, and ( 2) selects a node with the exact probability distribution .
Revised:  A DRW algorithm has the novel key features that (1) it always finishes in a number of hops bounded by the network diameter, and ( 2) selects a node with the .
Edit intent: clarity
Original: We propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if each of its partial derivatives keeps the same sign on tuples which differ on less than p positions.
Revised: We propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if none of its partial derivatives keeps the same sign on tuples which differ on less than p positions.
Edit intent: clarity
Original: We propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if each of its partial derivatives keeps the same sign on tuples which differ on less than p positions.
Revised: We propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if each of its partial derivatives changes in sign on tuples which differ on less than p positions.
Edit intent: clarity
Original: We propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if each of its partial derivatives keeps the same sign on tuples which differ on less than p positions.
Revised: We propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if each of its partial derivatives keeps the same sign on tuples which differ in less than p positions.
Edit intent: clarity
Original:  We provide further results relating these two notions, and present a classification of p-locally monotone functions, as well as of functions having p-permutable derivatives, in terms of certain forbidden "sections", i.e., functions which can be obtained by substituting variables for constants .
Revised:  We provide further results relating these two notions, and present a classification of p-locally monotone functions, as well as of functions having p-permutable derivatives, in terms of certain forbidden "sections", i.e., functions which can be obtained by substituting constants for variables .
Edit intent: fluency
Original: This paper introduces the Furthest Hyperplane Problem (FHP)  . Given a set of n points in %DIFDELCMD < \R%%% ^d , the objective is to produce the hyperplane (  through the origin) which maximizes the separation margin, that is, the minimal distance between the hyperplane and an input point.
Revised: This paper introduces the Furthest Hyperplane Problem (FHP) . Given a set of n points in %DIFDELCMD < \R%%% ^d , the objective is to produce the hyperplane ( passing through the origin) which maximizes the separation margin, that is, the minimal distance between the hyperplane and an input point.
Edit intent: clarity
Original: This paper introduces the Furthest Hyperplane Problem (FHP)  . Given a set of n points in %DIFDELCMD < \R%%% ^d , the objective is to produce the hyperplane (  through the origin) which maximizes the separation margin, that is, the minimal distance between the hyperplane and an input point.
Revised: This paper introduces the Furthest Hyperplane Problem (FHP) . Given a set of n points in %DIFDELCMD < \R%%% ^d , the objective is to produce the hyperplane ( through the origin) which maximizes the separation margin, that is, the minimal distance between the hyperplane and any input point.
Edit intent: clarity
Original: The classic Coupons-Collector Problem (CCP) is generalized  .
Revised: The classic Coupon-Collector Problem (CCP) is generalized .
Edit intent: fluency
Original:  CREs actively participate in many cellular processes that require accessibility of specific stretches of DNA which are packaged as chromatin.
Revised:  CREs actively participate in many cellular processes that require accessibility of specific segments of DNA which are packaged as chromatin.
Edit intent: clarity
Original:  We calculate the mean times for histone detachment .
Revised:  We calculate the mean time of traversal .
Edit intent: clarity
Original:   The equations in this family can be purely diffusive, purely hyperbolic or of convection-diffusion type, with frequency dependent convection , and the particular outcome will depend on the assumed scalings.
Revised:  The equations in this family can be purely diffusive, purely hyperbolic or of convection-diffusion type, with frequency dependent convection . The particular outcome will depend on the assumed scalings.
Edit intent: coherence
Original:  We also show that the convective approximation is related to the replicator dynamics and provide some estimate of how good is the convective approximation  .
Revised:  We also show that the convective approximation is related to the replicator dynamics and provide some estimate of how accurate is the convective approximation .
Edit intent: clarity
Original:  In particular, we show that the mode, but not the expected value, of the probability distribution is modeled by the replicator dynamics.
Revised:  In particular, we show that the mode, but not the expected value, of the probability distribution is modelled by the replicator dynamics.
Edit intent: clarity
Original: The dissimilarity of two polygonal curves can be measured using the Fr\'echet distance.
Revised: The similarity of two polygonal curves can be measured using the Fr\'echet distance.
Edit intent: fluency
Original:  We compute a constant factor approximation\eps to the minimum Fr\'echet distance over all possible such shortcuts, in near linear time, if the curve is c-packed and the number of shortcuts is small .
Revised:  We compute a constant factor approximation\eps)-approximation to the minimum Fr\'echet distance over all possible such shortcuts, in near linear time, if the curve is c-packed and the number of shortcuts is small .
Edit intent: clarity
Original:  To facilitate the new algorithm we develop several new tools: (A) A data-structure for preprocessing a curve (not necessarily c-packed) that supports (1+\eps)-approximate Fr\'echet distance queries between a subcurve (of the original curve) and a line segment.
Revised:  To facilitate the new algorithm we develop several new tools: (A) A data structure for preprocessing a curve (not necessarily c-packed) that supports (1+\eps)-approximate Fr\'echet distance queries between a subcurve (of the original curve) and a line segment.
Edit intent: fluency
Original:  (B) A near linear time algorithm that computes a permutation of the vertices of a curve, such that any prefix of 2k-1 vertices of this permutation, form an optimal approximation (up to a constant factor) to the original curve compared to any polygonal curve with k vertices, for any k > 0. (C) A data-structure for preprocessing a curve that supports O(1)-approximate Fr\'echet distance queries between a subcurve and a query polygonal curve.
Revised:  (B) A near linear time algorithm that computes a permutation of the vertices of a curve, such that any prefix of 2k-1 vertices of this permutation, form an optimal approximation (up to a constant factor) to the original curve compared to any polygonal curve with k vertices, for any k > 0. (C) A data structure for preprocessing a curve that supports O(1)-approximate Fr\'echet distance queries between a subcurve and a query polygonal curve.
Edit intent: fluency
Original:  (B) A near linear time algorithm that computes a permutation of the vertices of a curve, such that any prefix of 2k-1 vertices of this permutation, form an optimal approximation (up to a constant factor) to the original curve compared to any polygonal curve with k vertices, for any k > 0. (C) A data-structure for preprocessing a curve that supports O(1)-approximate Fr\'echet distance queries between a subcurve and a query polygonal curve.
Revised:  (B) A near linear time algorithm that computes a permutation of the vertices of a curve, such that any prefix of 2k-1 vertices of this permutation, form an optimal approximation (up to a constant factor) to the original curve compared to any polygonal curve with k vertices, for any k > 0. (C) A data-structure for preprocessing a curve that supports O(1)-approximate Fr\'echet distance queries between a subcurve and query polygonal curve.
Edit intent: fluency
Original:  To our knowledge, these are the first data-structures to support these kind of queries efficiently.
Revised:  To our knowledge, these are the first data structures to support these kind of queries efficiently.
Edit intent: fluency
Original: We investigate the complexity of the model checking problem for intuitionistic propositional logic IPC, and for the intuitionistic logics BPL ( basic propositional logic ), FPL ( formal propositional logic ), and KC ( Jankov's logic ) .
Revised: We investigate the complexity of the model checking problem for intuitionistic propositional logic IPC, basic propositional logic ), FPL ( formal propositional logic ), and KC ( Jankov's logic ) .
Edit intent: clarity
Original:  For BPL and FPL we reach P- hardness even on the implicational fragment with only one variable.
Revised:  For BPL and FPL we reach P-hardness even on the implicational fragment with only one variable.
Edit intent: fluency
Original: In this paper we prove a conjecture of Bulter and Graham Butler11  on the existence of a certain way of marking the lines {\em  in [k]^n for any prime k.
Revised: In this paper we prove a conjecture of Bulter and Graham Butler11 on the existence of certain way of marking the lines {\em in [k]^n for any prime k.
Edit intent: fluency
Original: In this paper we prove a conjecture of Bulter and Graham Butler11  on the existence of a certain way of marking the lines {\em  in [k]^n for any prime k.
Revised: In this paper we prove a conjecture of Bulter and Graham Butler11 on the existence of a certain way of marking the {\em in [k]^n for any prime k.
Edit intent: clarity
Original:  The conjecture states that there exists a way of marking each {\em  line} of [k]^n one point so that every point in [k]^n is marked exactly a or b times as long as the parameters (a,b,n,k) satisfy the condition that there are integers s, t such that s+t = k^n and as+bt = nk^{n-1}.
Revised:  The conjecture states that there exists a way to mark one point on each {\em line} of [k]^n one point so that every point in [k]^n is marked exactly a or b times as long as the parameters (a,b,n,k) satisfy the condition that there are integers s, t such that s+t = k^n and as+bt = nk^{n-1}.
Edit intent: clarity
Original:  The conjecture states that there exists a way of marking each {\em  line} of [k]^n one point so that every point in [k]^n is marked exactly a or b times as long as the parameters (a,b,n,k) satisfy the condition that there are integers s, t such that s+t = k^n and as+bt = nk^{n-1}.
Revised:  The conjecture states that there exists a way of marking each {\em coordinate line} of [k]^n one point so that every point in [k]^n is marked exactly a or b times as long as the parameters (a,b,n,k) satisfy the condition that there are integers s, t such that s+t = k^n and as+bt = nk^{n-1}.
Edit intent: fluency
Original:  The conjecture states that there exists a way of marking each {\em  line} of [k]^n one point so that every point in [k]^n is marked exactly a or b times as long as the parameters (a,b,n,k) satisfy the condition that there are integers s, t such that s+t = k^n and as+bt = nk^{n-1}.
Revised:  The conjecture states that there exists a way of marking each {\em line} in [k]^n one point so that every point in [k]^n is marked exactly a or b times as long as the parameters (a,b,n,k) satisfy the condition that there are integers s, t such that s+t = k^n and as+bt = nk^{n-1}.
Edit intent: clarity
Original:  The conjecture states that there exists a way of marking each {\em  line} of [k]^n one point so that every point in [k]^n is marked exactly a or b times as long as the parameters (a,b,n,k) satisfy the condition that there are integers s, t such that s+t = k^n and as+bt = nk^{n-1}.
Revised:  The conjecture states that there exists a way of marking each {\em line} of [k]^n , so that every point in [k]^n is marked exactly a or b times as long as the parameters (a,b,n,k) satisfy the condition that there are integers s, t such that s+t = k^n and as+bt = nk^{n-1}.
Edit intent: clarity
Original:  The conjecture states that there exists a way of marking each {\em  line} of [k]^n one point so that every point in [k]^n is marked exactly a or b times as long as the parameters (a,b,n,k) satisfy the condition that there are integers s, t such that s+t = k^n and as+bt = nk^{n-1}.
Revised:  The conjecture states that there exists a way of marking each {\em line} of [k]^n one point so that every point in [k]^n is marked exactly a or b times as long as the parameters (a,b,n,k) satisfies that there are integers s, t such that s+t = k^n and as+bt = nk^{n-1}.
Edit intent: clarity
Original:   Moreover, we prove the conjecture for the case when a=0 for general k . Bulter and Graham used a%DIFDELCMD < {\em %%% inflated markup method in \mbox{ \cite{Butler11}\hspace{0pt} . However, the construction of the base cases of the induction is far more complicated.
Revised:  Moreover, we prove the conjecture for the case when a=0 for general k %DIFDELCMD < {\em %%% inflated markup method in \mbox{ \cite{Butler11}\hspace{0pt} . However, the construction of the base cases of the induction is far more complicated.
Edit intent: coherence
Original:   Moreover, we prove the conjecture for the case when a=0 for general k . Bulter and Graham used a%DIFDELCMD < {\em %%% inflated markup method in \mbox{ \cite{Butler11}\hspace{0pt} . However, the construction of the base cases of the induction is far more complicated.
Revised:  Moreover, we prove the conjecture for the case when a=0 for general k . Bulter and Graham used a%DIFDELCMD < {\em %%% method in \mbox{ \cite{Butler11}\hspace{0pt} . However, the construction of the base cases of the induction is far more complicated.
Edit intent: coherence
Original:   Moreover, we prove the conjecture for the case when a=0 for general k . Bulter and Graham used a%DIFDELCMD < {\em %%% inflated markup method in \mbox{ \cite{Butler11}\hspace{0pt} . However, the construction of the base cases of the induction is far more complicated.
Revised:  Moreover, we prove the conjecture for the case when a=0 for general k . Bulter and Graham used a%DIFDELCMD < {\em %%% inflated markup }\hspace{0pt} . However, the construction of the base cases of the induction is far more complicated.
Edit intent: coherence
Original:  Here we introduce a characteristic function which classifies the points of }%DIFDELCMD < [%%% k ^n and has some desired symmetrical property.
Revised:  Here we introduce a characteristic function which classifies the points of }%DIFDELCMD < [%%% ^n and has some desired symmetrical property.
Edit intent: fluency
Original: A fuzzy linear system with crisp coefficient matrix and with an arbitrary fuzzy number in parametric form on the right-hand side is investigated .
Revised: We consider a fuzzy linear system with crisp coefficient matrix and with an arbitrary fuzzy number in parametric form on the right-hand side is investigated .
Edit intent: clarity
Original: A fuzzy linear system with crisp coefficient matrix and with an arbitrary fuzzy number in parametric form on the right-hand side is investigated .
Revised: A fuzzy linear system with crisp coefficient matrix and with an arbitrary fuzzy number in parametric form on the right-hand side .
Edit intent: clarity
Original:  It is shown that the well-known existence and uniqueness theorem of a strong fuzzy solution is equivalent to the following: The coefficient matrix is the product of a permutation matrix and a diagonal matrix.
Revised:  It is known that the well-known existence and uniqueness theorem of a strong fuzzy solution is equivalent to the following: The coefficient matrix is the product of a permutation matrix and a diagonal matrix.
Edit intent: coherence
Original:  An existence and uniqueness theorem, which can be used on more general systems , is proved .
Revised:  We prove an existence and uniqueness theorem, which can be used on more general systems , is proved .
Edit intent: clarity
Original:  An existence and uniqueness theorem, which can be used on more general systems , is proved .
Revised:  An existence and uniqueness theorem, which can be use on more general systems , is proved .
Edit intent: fluency
Original:  An existence and uniqueness theorem, which can be used on more general systems , is proved .
Revised:  An existence and uniqueness theorem, which can be used on more general systems .
Edit intent: clarity
Original:  The extension is non-trivial and a novel coupling of the requisite processes is introduced that is both easy to simulate and provides a small variance for the estimator.
Revised:  The extension is non-trivial , exploiting a coupling of the requisite processes is introduced that is both easy to simulate and provides a small variance for the estimator.
Edit intent: clarity
Original:  The extension is non-trivial and a novel coupling of the requisite processes is introduced that is both easy to simulate and provides a small variance for the estimator.
Revised:  The extension is non-trivial and a novel coupling of the requisite processes that is easy to simulate and provides a small variance for the estimator.
Edit intent: clarity
Original:  The extension is non-trivial and a novel coupling of the requisite processes is introduced that is both easy to simulate and provides a small variance for the estimator.
Revised:  The extension is non-trivial and a novel coupling of the requisite processes is introduced that is both easy to simulate while providing a small variance for the estimator.
Edit intent: coherence