wanyu/IteraTeR_v2 huggingface dataset:
Original:  In this paper, we show that already the containment problem for  linear sets is \log -hard (and therefore also \log -complete ) in \Pi_2^p . This holds even when we use a unary encoding for the numerical input parameters or when we restrict the problem to 1-dimensional linear sets ( i.e, linear sets in%DIFDELCMD < \nats%%% _0) . However, combining both restrictions  , the problem becomes solvable in polynomial time.
Revised:  In this paper, we show that already the containment problem for linear sets is \log -hard (and therefore also \log -complete in \Pi_2^p . This holds even when we use a unary encoding for the numerical input parameters or when we restrict the problem to 1-dimensional linear sets ( i.e, linear sets in%DIFDELCMD < \nats%%% _0) . However, combining both restrictions , the problem becomes solvable in polynomial time.
Edit intent: fluency
Original:  In this paper, we show that already the containment problem for  linear sets is \log -hard (and therefore also \log -complete ) in \Pi_2^p . This holds even when we use a unary encoding for the numerical input parameters or when we restrict the problem to 1-dimensional linear sets ( i.e, linear sets in%DIFDELCMD < \nats%%% _0) . However, combining both restrictions  , the problem becomes solvable in polynomial time.
Revised:  In this paper, we show that already the containment problem for linear sets is \log -hard (and therefore also \log -complete ) in \Pi_2^p (where hardness even holds for a unary encoding for the numerical input parameters or when we restrict the problem to 1-dimensional linear sets ( i.e, linear sets in%DIFDELCMD < \nats%%% _0) . However, combining both restrictions , the problem becomes solvable in polynomial time.
Edit intent: clarity
Original:  In this paper, we show that already the containment problem for  linear sets is \log -hard (and therefore also \log -complete ) in \Pi_2^p . This holds even when we use a unary encoding for the numerical input parameters or when we restrict the problem to 1-dimensional linear sets ( i.e, linear sets in%DIFDELCMD < \nats%%% _0) . However, combining both restrictions  , the problem becomes solvable in polynomial time.
Revised:  In this paper, we show that already the containment problem for linear sets is \log -hard (and therefore also \log -complete ) in \Pi_2^p . This holds even when we use a unary encoding of the numerical input parameters or when we restrict the problem to 1-dimensional linear sets ( i.e, linear sets in%DIFDELCMD < \nats%%% _0) . However, combining both restrictions , the problem becomes solvable in polynomial time.
Edit intent: fluency
Original:  In this paper, we show that already the containment problem for  linear sets is \log -hard (and therefore also \log -complete ) in \Pi_2^p . This holds even when we use a unary encoding for the numerical input parameters or when we restrict the problem to 1-dimensional linear sets ( i.e, linear sets in%DIFDELCMD < \nats%%% _0) . However, combining both restrictions  , the problem becomes solvable in polynomial time.
Revised:  In this paper, we show that already the containment problem for linear sets is \log -hard (and therefore also \log -complete ) in \Pi_2^p . This holds even when we use a unary encoding for the numerical input parameters ). In this paper, we show that already the containment problem for 1-dimensional linear sets ( i.e, linear sets in%DIFDELCMD < \nats%%% _0) . However, combining both restrictions , the problem becomes solvable in polynomial time.
Edit intent: coherence
Original:  In this paper, we show that already the containment problem for  linear sets is \log -hard (and therefore also \log -complete ) in \Pi_2^p . This holds even when we use a unary encoding for the numerical input parameters or when we restrict the problem to 1-dimensional linear sets ( i.e, linear sets in%DIFDELCMD < \nats%%% _0) . However, combining both restrictions  , the problem becomes solvable in polynomial time.
Revised:  In this paper, we show that already the containment problem for linear sets is \log -hard (and therefore also \log -complete ) in \Pi_2^p . This holds even when we use a unary encoding for the numerical input parameters or when we restrict the problem to 1-dimensional linear sets ( %DIFDELCMD < \nats%%% _0) . However, combining both restrictions , the problem becomes solvable in polynomial time.
Edit intent: coherence
Original: We reconsider the haploid deterministic mutation-selection equation with two types.
Revised: We reconsider the deterministic haploid mutation-selection equation with two types.
Edit intent: fluency
Original:  We present a monitoring and network resource configuration scheme to include hardware monitoring in both Ethernet and Optical layers.
Revised:  A monitoring and network resource configuration scheme to include hardware monitoring in both Ethernet and Optical layers.
Edit intent: clarity
Original:  We present a monitoring and network resource configuration scheme to include hardware monitoring in both Ethernet and Optical layers.
Revised:  We present a monitoring and network resource configuration scheme is proposed to include the hardware monitoring in both Ethernet and Optical layers.
Edit intent: clarity
Original:  The scheme also depicts the data and control interactions among multiple network layers under  software defined network (SDN) background, as well as the application that analyse the monitored data obtained from the database.
Revised:  The scheme depicts the data and control interactions among multiple network layers under software defined network (SDN) background, as well as the application that analyse the monitored data obtained from the database.
Edit intent: clarity
Original:  The scheme also depicts the data and control interactions among multiple network layers under  software defined network (SDN) background, as well as the application that analyse the monitored data obtained from the database.
Revised:  The scheme also depicts the data and control interactions among multiple network layers under the software defined network (SDN) background, as well as the application that analyse the monitored data obtained from the database.
Edit intent: fluency
Original:  The scheme also depicts the data and control interactions among multiple network layers under  software defined network (SDN) background, as well as the application that analyse the monitored data obtained from the database.
Revised:  The scheme also depicts the data and control interactions among multiple network layers under software defined network (SDN) background, as well as the application that analyses the monitored data obtained from the database.
Edit intent: fluency
Original:  In addition, a re-configuration algorithm is described to adaptively modify the composition of virtual optical networks based on two criteria : (i) according to the monitored Ethernet traffic, a re-configuration is made in Ethernet layer to groom the traffic, and (ii) depends on the monitored optical transmission quality of transmission (QoT), a reconfiguration is made in optical layer to modify the creation of virtual transceivers within the V-BVT.
Revised:  In addition, a re-configuration algorithm to adaptively modify the composition of virtual optical networks based on two criteria : (i) according to the monitored Ethernet traffic, a re-configuration is made in Ethernet layer to groom the traffic, and (ii) depends on the monitored optical transmission quality of transmission (QoT), a reconfiguration is made in optical layer to modify the creation of virtual transceivers within the V-BVT.
Edit intent: clarity
Original:  The outcome from the algorithm is executed by the SDN control through OpenFlow (OF) extensions , and a holistic (re-)configuration across both layers in Ethernet switches and V-BVTs are presented and studied .
Revised:  The outcome from the algorithm is executed by the SDN control through OpenFlow (OF) extensions for a holistic (re-)configuration across both layers in Ethernet switches and V-BVTs are presented and studied .
Edit intent: coherence
Original:  The outcome from the algorithm is executed by the SDN control through OpenFlow (OF) extensions , and a holistic (re-)configuration across both layers in Ethernet switches and V-BVTs are presented and studied .
Revised:  The outcome from the algorithm is executed by the SDN control through OpenFlow (OF) extensions , and a holistic (re-)configuration across both layers in Ethernet switches and V-BVTs .
Edit intent: coherence
Original:  We then present various real-world applications to show how the unique properties of SGD make it easier to produce constrained layouts than previous approaches.
Revised:  We then show how the unique properties of SGD make it easier to produce constrained layouts than previous approaches.
Edit intent: clarity
Original:  Deciding the existence of a tiling with L-trominoes for an arbitrary region in general is NP-complete, nonetheless, we indentify restrictions to the problem where either it remains NP-complete or it has a polynomial time algorithm.
Revised:  Deciding the existence of a tiling with L-trominoes for an arbitrary region in general is NP-complete, nonetheless, we identify restrictions to the problem where either it remains NP-complete or it has a polynomial time algorithm.
Edit intent: fluency
Original:  Deciding the existence of a tiling with L-trominoes for an arbitrary region in general is NP-complete, nonetheless, we indentify restrictions to the problem where either it remains NP-complete or it has a polynomial time algorithm.
Revised:  Deciding the existence of a tiling with L-trominoes for an arbitrary region in general is NP-complete, nonetheless, we indentify restrictions to the problem where it either remains NP-complete or it has a polynomial time algorithm.
Edit intent: fluency
Original:  Deciding the existence of a tiling with L-trominoes for an arbitrary region in general is NP-complete, nonetheless, we indentify restrictions to the problem where either it remains NP-complete or it has a polynomial time algorithm.
Revised:  Deciding the existence of a tiling with L-trominoes for an arbitrary region in general is NP-complete, nonetheless, we indentify restrictions to the problem where either it remains NP-complete or has a polynomial time algorithm.
Edit intent: fluency
Original:  First we show that an aztec diamond of order n always has an L-tromino tiling if and only if n(n+1)\equiv 0%DIFDELCMD < \mod %%% 3 ;
Revised:  First , we characterize the possibility of when an Aztec rectangle has an L-tromino tiling if and only if n(n+1)\equiv 0%DIFDELCMD < \mod %%% 3 ;
Edit intent: clarity
Original:  First we show that an aztec diamond of order n always has an L-tromino tiling if and only if n(n+1)\equiv 0%DIFDELCMD < \mod %%% 3 ;
Revised:  First we show that an aztec diamond of order n always has an L-tromino tiling %DIFDELCMD < \mod %%% 3 ;
Edit intent: clarity
Original:  Then  we study tilings of arbitrary regions where only 180^\circ rotations of L-trominoes are available.
Revised:  Then , we study tilings of arbitrary regions where only 180^\circ rotations of L-trominoes are available.
Edit intent: fluency
Original:  For this particular case we show that deciding the existence of a tiling remains NP-complete , yet, if a region contains certain so-called "forbidden polyominoes" as subregions, then there exists a polynomial time algorithm for deciding a tiling.
Revised:  For this particular case we show that deciding the existence of a tiling remains NP-complete ; yet, if a region contains certain so-called "forbidden polyominoes" as subregions, then there exists a polynomial time algorithm for deciding a tiling.
Edit intent: fluency
Original:  yet, if a region contains certain so-called "forbidden polyominoes" as subregions, then there exists a polynomial time algorithm for deciding a tiling.
Revised:  yet, if a region contains certain so-called `forbidden polyominoes' as subregions, then there exists a polynomial time algorithm for deciding a tiling.
Edit intent: fluency
Original: In this work we study tilings of regions in the square lattice with L-shaped trominoes.
Revised: We study tilings of regions in the square lattice with L-shaped trominoes.
Edit intent: clarity
Original:  First, we characterize the possibility of when an Aztec rectangle has an L-tromino tiling, and hence also an Aztec diamond ;
Revised:  First, we characterize the possibility of when an Aztec rectangle and an Aztec diamond ;
Edit intent: clarity
Original:  yet, if a region  contains certain so-called `forbidden polyominoes' as subregions , then there exists a polynomial time algorithm for deciding a tiling.
Revised:  yet, if a region does not contains certain so-called `forbidden polyominoes' as subregions , then there exists a polynomial time algorithm for deciding a tiling.
Edit intent: clarity
Original:  yet, if a region  contains certain so-called `forbidden polyominoes' as subregions , then there exists a polynomial time algorithm for deciding a tiling.
Revised:  yet, if a region contains certain so-called "forbidden polyominoes" as sub-regions , then there exists a polynomial time algorithm for deciding a tiling.
Edit intent: fluency
Original:  Despite promising empirical performance , most of these methods are derived from heuristic considerations and therefore still lack theoretical justification.
Revised:  Despite promising empirical performances , most of these methods are derived from heuristic considerations and therefore still lack theoretical justification.
Edit intent: fluency
Original:  We quantify the strength of local connectivity by a global parameter and relate it to more common network statistics such as  clustering coefficient and Ricci curvature.
Revised:  We quantify the strength of local connectivity by a global parameter and relate it to more common network statistics such as the clustering coefficient and Ricci curvature.
Edit intent: fluency
Original:  We quantify the strength of local connectivity by a global parameter and relate it to more common network statistics such as  clustering coefficient and Ricci curvature.
Revised:  We quantify the strength of local connectivity by a global parameter and relate it to more common network statistics such as clustering coefficient and network curvature.
Edit intent: clarity
Original:  Based on this result, we also derive a condition under which a hypergraph can be sampled and reduced to a weighted network .
Revised:  Based on this result, we also provide sufficient conditions under which random networks and hypergraphs can be sampled and reduced to a weighted network .
Edit intent: clarity
Original:  Based on this result, we also derive a condition under which a hypergraph can be sampled and reduced to a weighted network .
Revised:  Based on this result, we also derive a condition under which a hypergraph can be sampled efficiently .
Edit intent: clarity
Original:  This is problematic because TM is currently available, either natively or via extensions, in widely-used architectures and languages such as x86, Power, and C++ , all of which have weak memory models.
Revised:  This is problematic because such widely-used architectures and languages such as x86, Power, and C++ , all of which have weak memory models.
Edit intent: clarity
Original:  This is problematic because TM is currently available, either natively or via extensions, in widely-used architectures and languages such as x86, Power, and C++ , all of which have weak memory models.
Revised:  This is problematic because TM is currently available, either natively or via extensions, in widely-used architectures and languages as x86, Power, and C++ , all of which have weak memory models.
Edit intent: fluency
Original:  Our work aims to provide an formal understanding of the interplay between weak memory and TM , without which, programmers cannot robustly reason about programs that use both of these important concurrent programming constructs.
Revised:  Our work aims to clarify the interplay between weak memory and TM , without which, programmers cannot robustly reason about programs that use both of these important concurrent programming constructs.
Edit intent: clarity
Original:  It was observed that  Snort triggered a high rate of false positive alarms.
Revised:  It was observed that the Snort triggered a high rate of false positive alarms.
Edit intent: fluency
Original:  To select the best performing algorithm for the Snort adaptive plug-in, an empirical study was carried out with different learning algorithms and Support Vector Machine (SVM) was selected.
Revised:  To select the best performing algorithm for Snort adaptive plug-in, an empirical study was carried out with different learning algorithms and Support Vector Machine (SVM) was selected.
Edit intent: fluency
Original:  But the best result was achieved using an optimized SVM with the firefly algorithm with FPR (false positive rate) as 8.6\% and FNR (false negative rate) as 2.2\%, which is a good result.
Revised:  But the best result was achieved using an optimised SVM with firefly algorithm with FPR (false positive rate) as 8.6\% and FNR (false negative rate) as 2.2\%, which is a good result.
Edit intent: clarity
Original:  The novelty of this work is the performance comparison of two IDSs at 10 Gbps and the application of hybrid and optimized machine learning algorithms to Snort.
Revised:  The novelty of this work is the performance comparison of two IDSs at 10 Gbps and the application of hybrid and optimised machine learning algorithms to Snort.
Edit intent: fluency
Original:  We further demonstrate that this problem can be overcome by using deterministic recurrent neural networks as sources of stochasticity , exploiting the decorrelating effect of inhibitory feedback.
Revised:  We demonstrate that this problem can be overcome by using deterministic recurrent neural networks as sources of stochasticity , exploiting the decorrelating effect of inhibitory feedback.
Edit intent: clarity
Original:  We further demonstrate that this problem can be overcome by using deterministic recurrent neural networks as sources of stochasticity , exploiting the decorrelating effect of inhibitory feedback.
Revised:  We further demonstrate that this problem can be overcome by using deterministic recurrent neural networks as sources of uncorrelated noise , exploiting the decorrelating effect of inhibitory feedback.
Edit intent: clarity
Original:  We test the proposed framework for a diverse set of  networks with different dimensionalities and entropies .
Revised:  We successfully apply the proposed framework for a diverse set of networks with different dimensionalities and entropies .
Edit intent: clarity
Original:  We test the proposed framework for a diverse set of  networks with different dimensionalities and entropies .
Revised:  We test the proposed framework to a diverse set of networks with different dimensionalities and entropies .
Edit intent: fluency
Original:  A network reproducing handwritten digits with distinct predefined frequencies demonstrates the practical relevance .
Revised:  A network reproducing handwritten digits with distinct predefined frequencies .
Edit intent: clarity
Original:  In this Letter we describe the results of novel lattice-free Lotka-Volterra stochastic simulations, showing that , contrary to previous claims, the emergence of spiral patterns does occur for sufficiently high values of the (conserved) total density of individuals.
Revised:  In this Letter we describe the results of off-lattice Lotka-Volterra stochastic simulations, showing that , contrary to previous claims, the emergence of spiral patterns does occur for sufficiently high values of the (conserved) total density of individuals.
Edit intent: clarity
Original:  In this Letter we describe the results of novel lattice-free Lotka-Volterra stochastic simulations, showing that , contrary to previous claims, the emergence of spiral patterns does occur for sufficiently high values of the (conserved) total density of individuals.
Revised:  In this Letter we describe the results of novel lattice-free Lotka-Volterra stochastic simulations, showing that the emergence of spiral patterns does occur for sufficiently high values of the (conserved) total density of individuals.
Edit intent: clarity
Original: Although to date the millimeter wave (mmWave) band is underutilized, the large spectrum in this band has the potential to define a new era of wireless communications.
Revised: The key obstacle to achieving the full potential of the millimeter wave (mmWave) band is underutilized, the large spectrum in this band has the potential to define a new era of wireless communications.
Edit intent: clarity
Original:  In this article  we present a new architecture for mmWave MIMO communications.
Revised:  In this article , we present a new architecture for mmWave MIMO communications.
Edit intent: fluency
Original: A trajectory is a function that specifies the location of a moving entity through a certain time interval.
Edit intent: coherence
Original:  In this paper we study the problem of finding the hotspots of polygonal two-dimensional trajectories,  regions in which the entity has spent a significant amount of time.
Revised:  In this paper we study the problem of finding hotspots of polygonal two-dimensional trajectories, regions in which the entity has spent a significant amount of time.
Edit intent: fluency
Original:  In this paper we study the problem of finding the hotspots of polygonal two-dimensional trajectories,  regions in which the entity has spent a significant amount of time.
Revised:  In this paper we study the problem of finding the hotspots of polygonal two-dimensional trajectories, i.e. regions in which the entity has spent a significant amount of time.
Edit intent: coherence
Original:  In this paper we study the problem of finding the hotspots of polygonal two-dimensional trajectories,  regions in which the entity has spent a significant amount of time.
Revised:  In this paper we study the problem of finding the hotspots of polygonal two-dimensional trajectories, regions in which a moving entity has spent a significant amount of time.
Edit intent: clarity
Original: In this paper we study the problem of finding hotspots of polygonal two-dimensional trajectories , i.e. regions in which a moving entity has spent a significant amount of time  .
Revised: In this paper we study the problem of finding hotspots , i.e. regions in which a moving entity has spent a significant amount of time .
Edit intent: clarity
Original:  We present an approximation algorithm with the time complexity O(n \log n) and approximation factor 1/4 for orthogonal trajectories, in which the entity moves in a direction parallel either to the x or to the y-axis .
Revised:  Limiting ourselves to the case in which the entity moves in a direction parallel either to the x or to the y-axis .
Edit intent: clarity
Original: Social network analysis provides meaningful information about behavior of network members that can be used in diverse applications such as classification, link prediction , etc. however , network analysis is computationally expensive because of feature learning for different applications.
Revised: Social network analysis provides meaningful information about behavior of network members that can be used for diverse applications such as classification, link prediction , etc. however , network analysis is computationally expensive because of feature learning for different applications.
Edit intent: fluency
Original: Social network analysis provides meaningful information about behavior of network members that can be used in diverse applications such as classification, link prediction , etc. however , network analysis is computationally expensive because of feature learning for different applications.
Revised: Social network analysis provides meaningful information about behavior of network members that can be used in diverse applications such as classification, link prediction . However , network analysis is computationally expensive because of feature learning for different applications.
Edit intent: coherence