wanyu/IteraTeR_v2 huggingface dataset:
Original:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal  \emph{ }\emph{  \emph{ \emph{  reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{  }\hspace{0pt} whether k}\emph{  .
Revised:  This paper proves the%DIFDELCMD < {\cal %%% -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal \emph{ }\emph{ \emph{ \emph{ reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{ }\hspace{0pt} whether k}\emph{ .
Edit intent: fluency
Original:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal  \emph{ }\emph{  \emph{ \emph{  reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{  }\hspace{0pt} whether k}\emph{  .
Revised:  This paper proves the%DIFDELCMD < {\cal %%% NP %DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal \emph{ }\emph{ \emph{ \emph{ reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{ }\hspace{0pt} whether k}\emph{ .
Edit intent: clarity
Original:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal  \emph{ }\emph{  \emph{ \emph{  reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{  }\hspace{0pt} whether k}\emph{  .
Revised:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% first showed thatFPkLNCC is {\cal \emph{ }\emph{ \emph{ \emph{ reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{ }\hspace{0pt} whether k}\emph{ .
Edit intent: coherence
Original:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal  \emph{ }\emph{  \emph{ \emph{  reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{  }\hspace{0pt} whether k}\emph{  .
Revised:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal NP \emph{ }\emph{ \emph{ \emph{ reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{ }\hspace{0pt} whether k}\emph{ .
Edit intent: fluency
Original:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal  \emph{ }\emph{  \emph{ \emph{  reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{  }\hspace{0pt} whether k}\emph{  .
Revised:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal \emph{ }even for\emph{ \emph{ \emph{ reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{ }\hspace{0pt} whether k}\emph{ .
Edit intent: clarity
Original:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal  \emph{ }\emph{  \emph{ \emph{  reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{  }\hspace{0pt} whether k}\emph{  .
Revised:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal \emph{ }\emph{ by reducing from the\emph{ \emph{ reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{ }\hspace{0pt} whether k}\emph{ .
Edit intent: fluency
Original:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal  \emph{ }\emph{  \emph{ \emph{  reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{  }\hspace{0pt} whether k}\emph{  .
Revised:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal \emph{ }\emph{ \emph{ \emph{LNCC reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{ }\hspace{0pt} whether k}\emph{ .
Edit intent: fluency
Original:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal  \emph{ }\emph{  \emph{ \emph{  reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{  }\hspace{0pt} whether k}\emph{  .
Revised:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal \emph{ }\emph{ \emph{ \emph{ reduction from the 3 Occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{ }\hspace{0pt} whether k}\emph{ .
Edit intent: fluency
Original:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal  \emph{ }\emph{  \emph{ \emph{  reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{  }\hspace{0pt} whether k}\emph{  .
Revised:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal \emph{ }\emph{ \emph{ \emph{ reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ and 2\emph{ }\hspace{0pt} whether k}\emph{ .
Edit intent: coherence
Original:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal  \emph{ }\emph{  \emph{ \emph{  reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{  }\hspace{0pt} whether k}\emph{  .
Revised:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal \emph{ }\emph{ \emph{ \emph{ reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{ }\hspace{0pt} whether k}\emph{LNCC .
Edit intent: fluency
Original:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal  \emph{ }\emph{  \emph{ \emph{  reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{  }\hspace{0pt} whether k}\emph{  .
Revised:  This paper proves the%DIFDELCMD < {\cal %%% NP -completeness of kNCP for any fixed k%DIFDELCMD < \geq3 %%% by giving aFPkLNCC is {\cal \emph{ }\emph{ \emph{ \emph{ reduction from the 3 occurrence 3-Satisfiability (\emph{3O3SAT}) problem . Compared to the fact that the negative cycle detection problem is polynomial solvable and the k-cycle problem is fixed-parameter tractable with respect to k, the hardness result for kNCP seems interesting\emph{ \emph{ }\hspace{0pt} whether k}\emph{ admits polynomial-time algorithms .
Edit intent: clarity
Original:  Lastly, we define a very restricted class of label decoders using first-order logic that already contains many natural graph classes such as forests and interval graphs.
Revised:  Lastly, we define a more restrictive class of label decoders using first-order logic that already contains many natural graph classes such as forests and interval graphs.
Edit intent: clarity
Original: Voltage-gated calcium channels (VGCCs)  are present in all mammalian central neurons, controlling presynaptic release of transmitter, postsynaptic signalling and synaptic integration.
Revised: Voltage-gated calcium channels (VGCCs) . They are present in all mammalian central neurons, controlling presynaptic release of transmitter, postsynaptic signalling and synaptic integration.
Edit intent: coherence
Original: Voltage-gated calcium channels (VGCCs)  are present in all mammalian central neurons, controlling presynaptic release of transmitter, postsynaptic signalling and synaptic integration.
Revised: Voltage-gated calcium channels (VGCCs) are present in all mammalian central neurons, controlling presynaptic release of transmitter, postsynaptic signaling and synaptic integration.
Edit intent: fluency
Original:  The amplitudes of their single open-channel currents in a physiological concentration of extracellular calcium, however, are  not well determined , being too small to resolve directly in patch-clamp recordings .
Revised:  The amplitudes of their single channel currents in a physiological concentration of extracellular calcium, however, are not well determined , being too small to resolve directly in patch-clamp recordings .
Edit intent: clarity
Original:  The amplitudes of their single open-channel currents in a physiological concentration of extracellular calcium, however, are  not well determined , being too small to resolve directly in patch-clamp recordings .
Revised:  The amplitudes of their single open-channel currents in a physiological concentration of extracellular calcium, however, are small and not well determined , being too small to resolve directly in patch-clamp recordings .
Edit intent: coherence
Original:  The amplitudes of their single open-channel currents in a physiological concentration of extracellular calcium, however, are  not well determined , being too small to resolve directly in patch-clamp recordings .
Revised:  The amplitudes of their single open-channel currents in a physiological concentration of extracellular calcium, however, are not well determined .
Edit intent: coherence
Original:  However, measurement of this quantity is essential for estimating numbers of functional VGCCs in the membrane and the size of channel-associated calcium signalling domains, and for understanding the stochastic nature of calcium signalling .
Revised:  However, measurement of this quantity is essential for estimating numbers of functional VGCCs in the membrane and the size of channel-associated calcium signaling domains, and for understanding the stochastic nature of calcium signalling .
Edit intent: fluency
Original:  However, measurement of this quantity is essential for estimating numbers of functional VGCCs in the membrane and the size of channel-associated calcium signalling domains, and for understanding the stochastic nature of calcium signalling .
Revised:  However, measurement of this quantity is essential for estimating numbers of functional VGCCs in the membrane and the size of channel-associated calcium signalling domains, and for understanding the stochastic nature of calcium signaling .
Edit intent: fluency
Original:  Here, we recorded the voltage-gated calcium channel current in nucleated patches from layer 5 pyramidal neurons in rat neocortex, in physiological external calcium (1-2 mM).
Revised:  Here, we recorded the VGCC current in nucleated patches from layer 5 pyramidal neurons in rat neocortex, in physiological external calcium (1-2 mM).
Edit intent: clarity
Original:  In order to reliably separate the calcium current fluctuations from other background currents for fluctuation analysis, despite their small amplitude and rapid rundown , we developed a method using band-pass filtered current responses to ramp membrane potential stimulation .
Revised:  In order to reliably separate the calcium current fluctuations from other background currents for fluctuation analysis, despite their small amplitude and rapid rundown , we developed a method using band-pass filtering .
Edit intent: clarity
Original:  We validated the accuracy of the method by analysing simulated data.
Revised:  We validated the accuracy of the method by analyzing simulated data.
Edit intent: fluency
Original:  At  external calcium concentration of 1 mM, and a membrane potential of -20 to -15 mV, we found that  single channel current amplitude was about 0.04 pA, increasing to 0.065 pA at 2 mM external calcium, and 0.12 pA at 5 mM.
Revised:  At an external calcium concentration of 1 mM, and a membrane potential of -20 to -15 mV, we found that single channel current amplitude was about 0.04 pA, increasing to 0.065 pA at 2 mM external calcium, and 0.12 pA at 5 mM.
Edit intent: fluency
Original:  At  external calcium concentration of 1 mM, and a membrane potential of -20 to -15 mV, we found that  single channel current amplitude was about 0.04 pA, increasing to 0.065 pA at 2 mM external calcium, and 0.12 pA at 5 mM.
Revised:  At external calcium concentration of 1 mM, and a membrane potential of -20 mV, we found that single channel current amplitude was about 0.04 pA, increasing to 0.065 pA at 2 mM external calcium, and 0.12 pA at 5 mM.
Edit intent: clarity
Original:  At  external calcium concentration of 1 mM, and a membrane potential of -20 to -15 mV, we found that  single channel current amplitude was about 0.04 pA, increasing to 0.065 pA at 2 mM external calcium, and 0.12 pA at 5 mM.
Revised:  At external calcium concentration of 1 mM, and a membrane potential of -20 to -15 mV, we found that the average single channel current amplitude was about 0.04 pA, increasing to 0.065 pA at 2 mM external calcium, and 0.12 pA at 5 mM.
Edit intent: clarity
Original:  The results demonstrate that single channel current amplitude of native voltage-gated calcium channels can be resolved accurately and straightforwardly .
Revised:  The results demonstrate that single channel current amplitude of native VGCCs can be resolved accurately and straightforwardly .
Edit intent: clarity
Original:  However, measurement of this quantity is essential for estimating numbers of functional VGCCs in the membrane and the size of channel-associated calcium signaling domains, and for understanding the stochastic nature of calcium signaling.
Revised:  But measurement of this quantity is essential for estimating numbers of functional VGCCs in the membrane and the size of channel-associated calcium signaling domains, and for understanding the stochastic nature of calcium signaling.
Edit intent: coherence
Original:  We therefore developed a novel, more robust method, using voltage ramp stimulation, mean current fitting of individual current responses and band-pass filtering.
Revised:  We therefore developed a more robust method, using voltage ramp stimulation, mean current fitting of individual current responses and band-pass filtering.
Edit intent: clarity
Original:  We therefore developed a novel, more robust method, using voltage ramp stimulation, mean current fitting of individual current responses and band-pass filtering.
Revised:  We therefore developed a novel, more robust method, using mean current fitting of individual current responses and band-pass filtering.
Edit intent: coherence
Original:  When machining a pocket in a solid piece of material  such as steel  using a rough tool in a milling machine, sharp convex corners of the pocket cannot be done properly, but have to be left for finer tools that are more expensive to use.
Revised:  When cutting away a region from a solid piece of material such as steel using a rough tool in a milling machine, sharp convex corners of the pocket cannot be done properly, but have to be left for finer tools that are more expensive to use.
Edit intent: clarity
Original:  When machining a pocket in a solid piece of material  such as steel  using a rough tool in a milling machine, sharp convex corners of the pocket cannot be done properly, but have to be left for finer tools that are more expensive to use.
Revised:  When machining a pocket in a solid piece of material -- such as steel using a rough tool in a milling machine, sharp convex corners of the pocket cannot be done properly, but have to be left for finer tools that are more expensive to use.
Edit intent: fluency
Original:  When machining a pocket in a solid piece of material  such as steel  using a rough tool in a milling machine, sharp convex corners of the pocket cannot be done properly, but have to be left for finer tools that are more expensive to use.
Revised:  When machining a pocket in a solid piece of material such as steel using a rough tool in a milling machine, sharp convex corners of the region cannot be done properly, but have to be left for finer tools that are more expensive to use.
Edit intent: clarity
Original:  We want to determine a tool path that maximizes the use of the rough tool.
Revised:  We want to determine a toolpath that maximizes the use of the rough tool.
Edit intent: fluency
Original:  Mathematically, this boils down to the following problem . Given a simply-connected set of points P in the plane such that the boundary \partial P is a curvilinear polygon consisting of n line segments and circular arcs of arbitrary radii, compute the maximum subset Q\subseteq P consisting of simply-connected sets where the boundary of each set is a curve with bounded convex curvature.
Revised:  In order to formulate the problem in mathematical terms, we introduce the notion of bounded convex curvature.
Edit intent: coherence
Original:   The difference in the requirement to left- and right-curvature is a natural consequence of different conditions when machining convex and concave areas of the pocket .
Revised:  The difference in the requirement to left- and right-curvature is a natural consequence of different conditions when machining convex and concave areas of Q .
Edit intent: clarity
Original:  We devise an algorithm to compute the unique maximum such set Q . The algorithm runs in  O(n \log n) time and uses O(n) space.
Revised:  We devise an algorithm to compute the unique maximum such set Q . The algorithm runs in time O(n \log n) time and uses O(n) space.
Edit intent: clarity
Original:  Explicating the cost of treatment in terms of its efficacy, we conclude that the relative cost of successful versus unsuccessful treatment is bound from above by the probability of treatment failure .
Revised:  Notably, we obtain that, if the relative cost of successful versus unsuccessful treatment is bound from above by the probability of treatment failure .
Edit intent: coherence
Original:  This paper is the first of a series of two that deal with the problem of tracer coefficient estimation via compartmental modeling in an inverse problem framework.
Revised:  This paper is the first of a series of two that deal with the problem of tracer coefficient estimation via compartmental modelling in an inverse problem framework.
Edit intent: fluency
Original:  Specifically, here we discuss the identifiability problem for a general n-dimension compartmental system and provide uniqueness results in the case of two-compartment and three-compartment catenary models.
Revised:  Specifically, here we discuss the identifiability problem for a general n-dimension compartmental system and provide uniqueness results in the case of two-compartment and three-compartment compartmental models.
Edit intent: fluency
Original: Although database researchers have devoted considerable effort to helping database users formulate queries, many users still find it challenging to specify queries that involve joining tables.
Revised: Although researchers have devoted considerable effort to helping database users formulate queries, many users still find it challenging to specify queries that involve joining tables.
Edit intent: fluency
Original: Although database researchers have devoted considerable effort to helping database users formulate queries, many users still find it challenging to specify queries that involve joining tables.
Revised: Although database researchers have devoted considerable attention to helping database users formulate queries, many users still find it challenging to specify queries that involve joining tables.
Edit intent: clarity
Original:  To help users construct join queries for exploring relational databases, we propose Etable , a novel presentation data model that provides users with a presentation-level interactive view.
Revised:  To help users construct join queries for exploring relational databases, we propose ETable , a novel presentation data model that provides users with a presentation-level interactive view.
Edit intent: fluency