wanyu/IteraTeR_v2 huggingface dataset:
Original:  It is widely used in practice for a diverse set of applications.
Edit intent: coherence
Original:  A thread of research pioneered by Flajolet and Martin three decades ago initiated the design of highly effective approximate counting structures, which with size that is double logarithmic in the number of distinct keys provides estimates with a small relative error.
Revised:  A thread of research pioneered by Flajolet and Martin three decades ago culminated in the design of highly effective approximate counting structures, which with size that is double logarithmic in the number of distinct keys provides estimates with a small relative error.
Edit intent: clarity
Original:  A thread of research pioneered by Flajolet and Martin three decades ago initiated the design of highly effective approximate counting structures, which with size that is double logarithmic in the number of distinct keys provides estimates with a small relative error.
Revised:  A thread of research pioneered by Flajolet and Martin three decades ago initiated the design of optimal approximate counting sketches, which have size that is double logarithmic in the number of distinct keys provides estimates with a small relative error.
Edit intent: clarity
Original:  A thread of research pioneered by Flajolet and Martin three decades ago initiated the design of highly effective approximate counting structures, which with size that is double logarithmic in the number of distinct keys provides estimates with a small relative error.
Revised:  A thread of research pioneered by Flajolet and Martin three decades ago initiated the design of highly effective approximate counting structures, which with size that is double logarithmic in the number of distinct keys and provide estimates with a small relative error.
Edit intent: coherence
Original:  Moreover, the structures are mergeable/composable, which makes them suitable for streamed, parallel, or distributed computation.
Revised:  Moreover, the sketches are composable, and thus suitable for streamed, parallel, or distributed computation.
Edit intent: clarity
Original:  We present a novel framework that leverages these structures and their existing implementations to approximate any frequency statistics of the key frequency distribution , where a contribution of a key to the aggregate is concave and grows (sub)linearly with its frequency in the data .
Revised:  We consider here all statistics of the key frequency distribution , where a contribution of a key to the aggregate is concave and grows (sub)linearly with its frequency in the data .
Edit intent: clarity
Original:  We present a novel framework that leverages these structures and their existing implementations to approximate any frequency statistics of the key frequency distribution , where a contribution of a key to the aggregate is concave and grows (sub)linearly with its frequency in the data .
Revised:  We present a novel framework that leverages these structures and their existing implementations to approximate any frequency statistics of the frequency distribution of keys , where a contribution of a key to the aggregate is concave and grows (sub)linearly with its frequency in the data .
Edit intent: clarity
Original:  We present a novel framework that leverages these structures and their existing implementations to approximate any frequency statistics of the key frequency distribution , where a contribution of a key to the aggregate is concave and grows (sub)linearly with its frequency in the data .
Revised:  We present a novel framework that leverages these structures and their existing implementations to approximate any frequency statistics of the key frequency distribution , where a contribution of a key to the aggregate is concave and grows (sub)linearly with its frequency .
Edit intent: clarity
Original: Low-power wireless bus (LWB) is a highly efficient communication protocol for wireless sensor networks (WSN). A lack of open implementation for this protocol prompted the implementation of the protocol .
Revised: The low-power wireless bus (LWB) is a highly efficient communication protocol for wireless sensor networks (WSN). A lack of open implementation for this protocol prompted the implementation of the protocol .
Edit intent: clarity
Original: Low-power wireless bus (LWB) is a highly efficient communication protocol for wireless sensor networks (WSN). A lack of open implementation for this protocol prompted the implementation of the protocol .
Revised: Low-power wireless bus (LWB) is a highly efficient communication protocol for wireless sensor networks (WSN). However, a lack of open implementation for this protocol prompted the implementation of the protocol .
Edit intent: coherence
Original:  The BSDE generator function can be non-convex and needs not to satisfy classical global Lipschitz conditions in the jump integrand.
Revised:  The BSDE generator function can be non convex and needs not to satisfy classical global Lipschitz conditions in the jump integrand.
Edit intent: fluency
Original:  The BSDE generator function can be non-convex and needs not to satisfy classical global Lipschitz conditions in the jump integrand.
Revised:  The BSDE generator function can be non-convex and needs not to satisfy global Lipschitz conditions in the jump integrand.
Edit intent: clarity
Original:  We contribute concrete criteria, that are easy to verify, and extended results for comparison and for existence and uniqueness of bounded solutions to BSDEs with jumps .
Revised:  We contribute concrete criteria, that are easy to verify, for results on existence and uniqueness of bounded solutions to BSDEs with jumps .
Edit intent: clarity
Original:  We contribute concrete criteria, that are easy to verify, for results on existence and uniqueness of bounded solutions to BSDEs with jumps, and on comparison and a priori L^{\infty}-bounds.
Revised:  We contribute concrete criteria, that are easy to verify, for results on existence and uniqueness of bounded solutions to BSDEs with jumps, and on comparison and a-priori L^{\infty}-bounds.
Edit intent: fluency
Original:  Furthermore, the incidence of melanoma has been rising by about 3\% per year, while the incidence of most common cancers is decreasing.
Revised:  Furthermore, the incidence of melanoma has been rising by about 3\% per year, whereas the incidence of most common cancers is decreasing.
Edit intent: coherence
Original:  A handful of targeted therapies have recently become available , though these drugs are expected to increase survival only by a few months in some patient groups before relapse .
Revised:  A handful of targeted therapies have recently become available , though these drugs are expected to increase survival only by a few months in metastatic patient groups before relapse .
Edit intent: clarity
Original:  It may be possible to effectively treat patients, if early diagnosis can be made when the tumor burden is still low.
Revised:  It may be possible if a diagnosis can be made when the tumor burden is still low.
Edit intent: clarity
Original: The Colouring problem is that of deciding whether a given graph G admits a (proper) k-colouring for a given integer k. A graph is (H_1,H_2)-free for a pair of graphs H_1,H_2 if it contains no induced subgraph isomorphic to H_1 or H_2.
Revised:  A graph is (H_1,H_2)-free for a pair of graphs H_1,H_2 if it contains no induced subgraph isomorphic to H_1 or H_2.
Edit intent: coherence
Original:  The complement of a graph H has the same vertices as H and an edge between two distinct vertices if and only if these  vertices are not adjacent in H. By combining new and known results we classify the computational complexity of Colouring  for (H, )-free graphs except when H=sP_1+P_3  or H=sP_1+P_4 for s\geq 2.
Revised:  The complement of a graph H has the same vertices as H and an edge between two distinct vertices if and only if these two vertices are not adjacent in H. By combining new and known results we classify the computational complexity of Colouring for (H, )-free graphs except when H=sP_1+P_3 or H=sP_1+P_4 for s\geq 2.
Edit intent: fluency
Original:  The complement of a graph H has the same vertices as H and an edge between two distinct vertices if and only if these  vertices are not adjacent in H. By combining new and known results we classify the computational complexity of Colouring  for (H, )-free graphs except when H=sP_1+P_3  or H=sP_1+P_4 for s\geq 2.
Revised:  The complement of a graph H has the same vertices as H and an edge between two distinct vertices if and only if these vertices are not adjacent in H. By combining new and known results we classify the computational complexity of Colouring for (H, )-free graphs except when H=sP_1+P_3 for s\geq 3 or H=sP_1+P_4 for s\geq 2.
Edit intent: fluency
Original:  We continue a study into the complexity of Colouring and Clique Cover for (H_1,H_2)-free graphs by focusing on the case where their complexities coincide.
Revised:  We continue a study into the complexity of Colouring for (H_1,H_2)-free graphs by focusing on the case where their complexities coincide.
Edit intent: clarity
Original:  The complement of a graph Hhas the same vertices as H and an edge between two distinct vertices if and only if these two vertices are not adjacent in H  . By combining new and known results we classify the computational complexity of Colouring and Clique Cover for (H,H)-free graphs  except when H=sP_1+ P_3 for s\geq 3 or H=sP_1+P_4 for s\geq 2.
Revised:  The complement of a graph Hhas the same vertices as H and an edge between two distinct vertices if and only if these two vertices are not adjacent in H . By combining new and known results , we are able to classify the complexity of Colouring and Clique Cover for (H,H)-free graphs except when H=sP_1+ P_3 for s\geq 3 or H=sP_1+P_4 for s\geq 2.
Edit intent: clarity
Original:  The complement of a graph Hhas the same vertices as H and an edge between two distinct vertices if and only if these two vertices are not adjacent in H  . By combining new and known results we classify the computational complexity of Colouring and Clique Cover for (H,H)-free graphs  except when H=sP_1+ P_3 for s\geq 3 or H=sP_1+P_4 for s\geq 2.
Revised:  The complement of a graph Hhas the same vertices as H and an edge between two distinct vertices if and only if these two vertices are not adjacent in H . By combining new and known results we classify the computational complexity of Colouring and Clique Cover for (H,H)-free graphs for all cases except when H=sP_1+ P_3 for s\geq 3 or H=sP_1+P_4 for s\geq 2.
Edit intent: clarity
Original:  In particular,  we consider the Rips complex constructed out of a given metric graph, G . Such a complex, and hence shortest paths in it, represent the underlying metric space (whose discrete representation is the graph) more closely than what a graph would do .
Revised:  In particular, we consider the Rips complex constructed out of a given metric graph, G . Such a complex, and hence shortest paths in it, represent the underlying metric space more closely than what a graph would do .
Edit intent: clarity
Original:  In particular,  we consider the Rips complex constructed out of a given metric graph, G . Such a complex, and hence shortest paths in it, represent the underlying metric space (whose discrete representation is the graph) more closely than what a graph would do .
Revised:  In particular, we consider the Rips complex constructed out of a given metric graph, G . Such a complex, and hence shortest paths in it, represent the underlying metric space (whose discrete representation is the graph) more closely than what the graph does .
Edit intent: clarity
Original:  While discrete graph representations of continuous spaces is convenient for motion planning in configuration spaces of robotic systems, the metric induced in them by the ambient configuration space is  different from the metric of the configuration space itself.
Revised:  While discrete graph representations of continuous spaces is convenient for motion planning in configuration spaces of robotic systems, the metric induced in them by the ambient configuration space is significantly different from the metric of the configuration space itself.
Edit intent: clarity
Original:  We remedy this problem using a simplicial complex instead .
Revised:  We remedy this problem using the simplicial complex representation .
Edit intent: clarity
Original:  Our algorithm is local in nature, requiring only an abstract graph, G=(V,E), and a cost/length function, d:E\rightarrow R_+, and no other global information such as an embedding  is required.
Revised:  Our algorithm requires only an abstract graph, G=(V,E), and a cost/length function, d:E\rightarrow R_+, and no other global information such as an embedding is required.
Edit intent: coherence
Original:  Our algorithm is local in nature, requiring only an abstract graph, G=(V,E), and a cost/length function, d:E\rightarrow R_+, and no other global information such as an embedding  is required.
Revised:  Our algorithm is local in nature, requiring only an abstract graph, G=(V,E), and a cost/length function, d:E\rightarrow R_+, as inputs, and no global information such as an embedding is required.
Edit intent: clarity
Original:  The complexity of our algorithm is comparable to that of Dijkstra's search algorithm , but, as the results presented in this paper demonstrate, the shortest paths obtained using the proposed algorithm represent/approximate the geodesic paths in the original metric space much more closely.
Revised:  The complexity of our algorithm is comparable to that of Dijkstra's search , but, as the results presented in this paper demonstrate, the shortest paths obtained using the proposed algorithm represent/approximate the geodesic paths in the original metric space much more closely.
Edit intent: fluency
Original:  The complexity of our algorithm is comparable to that of Dijkstra's search algorithm , but, as the results presented in this paper demonstrate, the shortest paths obtained using the proposed algorithm represent/approximate the geodesic paths in the original metric space much more closely.
Revised:  The complexity of our algorithm is comparable to that of Dijkstra's search algorithm , but, as the results presented in this paper demonstrate, the shortest paths obtained using the proposed algorithm represent/approximate the geodesic paths in the original metric space significantly more closely.
Edit intent: clarity
Original:  Pricing this type of bonds is a challenging task and no closed form solution exists in the literature.
Revised:  Pricing these type of bonds is a challenging task and no closed form solution exists in the literature.
Edit intent: fluency
Original:  In our approach, we adapt the payoff of such a bond in terms of the payoff of an Asian put option and present a new approach to derive model-independent bounds exploiting comonotonic theory as illustrated in prime1 0pt and \mbox{ Simon }0pt } for the pricing of Asian options.
Revised:  In our approach, we express the payoff of such a bond in terms of the payoff of an Asian put option and present a new approach to derive model-independent bounds exploiting comonotonic theory as illustrated in prime1 0pt and \mbox{ Simon }0pt } for the pricing of Asian options.
Edit intent: clarity
Original:  We carry out Monte Carlo simulations to estimate the bond price and illustrate the strength of the bounds.
Revised:  We carry out Monte Carlo simulations to estimate the bond price and illustrate the quality of the bounds.
Edit intent: clarity
Original:  But Manhattan structure can be hard to observe from  single image due to occlusion.
Revised:  But Manhattan structure can be hard to observe from a single image due to occlusion.
Edit intent: fluency
Original:  Our results on  Pascal3D+ dataset show that our methods can significantly outperform baseline methods.
Revised:  Our results on the Pascal3D+ dataset show that our methods can significantly outperform baseline methods.
Edit intent: fluency
Original:  By assuming an orthographic projection model, this paper addresses the estimation of 3D structures and camera projection using symmetry and/or Manhattan structure cues, for the two cases when the input is a single image or multiple images from the same category, e.g.  multiple different cars.
Revised:  By assuming an orthographic projection model, this paper addresses the estimation of 3D structures and camera projection using symmetry and/or Manhattan structure cues, which occur when the input is a single image or multiple images from the same category, e.g. multiple different cars.
Edit intent: clarity
Original:  By assuming an orthographic projection model, this paper addresses the estimation of 3D structures and camera projection using symmetry and/or Manhattan structure cues, for the two cases when the input is a single image or multiple images from the same category, e.g.  multiple different cars.
Revised:  By assuming an orthographic projection model, this paper addresses the estimation of 3D structures and camera projection using symmetry and/or Manhattan structure cues, for the two cases when the input is single- or multiple-image from the same category, e.g. multiple different cars.
Edit intent: fluency
Original:  By assuming an orthographic projection model, this paper addresses the estimation of 3D structures and camera projection using symmetry and/or Manhattan structure cues, for the two cases when the input is a single image or multiple images from the same category, e.g.  multiple different cars.
Revised:  By assuming an orthographic projection model, this paper addresses the estimation of 3D structures and camera projection using symmetry and/or Manhattan structure cues, for the two cases when the input is a single image or multiple images from the same category, e.g. , multiple different cars.
Edit intent: fluency
Original:  Specifically, analysis on  single image case implies that Manhattan alone is sufficient to recover the camera projection,  then the 3D structure can be reconstructed uniquely exploiting symmetry.
Revised:  Specifically, analysis on the single image case implies that Manhattan alone is sufficient to recover the camera projection, then the 3D structure can be reconstructed uniquely exploiting symmetry.
Edit intent: fluency
Original:  Specifically, analysis on  single image case implies that Manhattan alone is sufficient to recover the camera projection,  then the 3D structure can be reconstructed uniquely exploiting symmetry.
Revised:  Specifically, analysis on single image case implies that Manhattan alone is sufficient to recover the camera projection, and then the 3D structure can be reconstructed uniquely exploiting symmetry.
Edit intent: coherence
Original:  But Manhattan structure can be hard to observe from a single image due to occlusion.
Revised:  However, Manhattan structure can be hard to observe from a single image due to occlusion.
Edit intent: coherence
Original:  But Manhattan structure can be hard to observe from a single image due to occlusion.
Revised:  But Manhattan structure can be difficult to observe from a single image due to occlusion.
Edit intent: fluency
Original:  Hence , we extend to the multiple image case which can also exploit symmetry but does not require Manhattan axes.
Revised:  To this end , we extend to the multiple image case which can also exploit symmetry but does not require Manhattan axes.
Edit intent: coherence
Original:  Hence , we extend to the multiple image case which can also exploit symmetry but does not require Manhattan axes.
Revised:  Hence , we extend to the multiple-image case which can also exploit symmetry but does not require Manhattan axes.
Edit intent: fluency
Original:  We propose a new rigid structure from motion method, exploiting symmetry , using multiple images from the same category as input.
Revised:  We propose a novel rigid structure from motion method, exploiting symmetry , using multiple images from the same category as input.
Edit intent: clarity
Original:  We propose a new rigid structure from motion method, exploiting symmetry , using multiple images from the same category as input.
Revised:  We propose a new rigid structure from motion method, exploiting symmetry and using multiple images from the same category as input.
Edit intent: coherence
Original:  Our results on the Pascal3D+ dataset show that our methods can significantly outperform baseline methods.
Revised:  Experimental results on the Pascal3D+ dataset show that our methods can significantly outperform baseline methods.
Edit intent: fluency
Original:  Our results on the Pascal3D+ dataset show that our methods can significantly outperform baseline methods.
Revised:  Our results on the Pascal3D+ dataset show that our method significantly outperforms baseline methods.
Edit intent: clarity
Original:  In addition, we prove that f_2(G) \leq 310 when G is planar , which implies that the maximum adjacent closed vertex-distinguishing chromatic number of planar graphs is constant .
Revised:  In addition, we prove that f_2(G) \leq 310 when G is planar .
Edit intent: coherence
Original: While the Linked Data community provides many big and interlinked datasets, efficient usage of the knowledge is often limited by the need for domain experts to formulate the right SPARQL queries to answer questions.
Revised: Efficient usage of the knowledge is often limited by the need for domain experts to formulate the right SPARQL queries to answer questions.
Edit intent: coherence
Original: While the Linked Data community provides many big and interlinked datasets, efficient usage of the knowledge is often limited by the need for domain experts to formulate the right SPARQL queries to answer questions.
Revised: While the Linked Data community provides many big and interlinked datasets, efficient usage of the knowledge provided by the Linked Data community is often hindered by the need for domain experts to formulate the right SPARQL queries to answer questions.
Edit intent: clarity
Original:  For each new question they have to decide which datasets are suitable and in which terminology and modelling style to phrase the SPARQL query.
Revised:  For new questions they have to decide which datasets are suitable and in which terminology and modelling style to phrase the SPARQL query.
Edit intent: clarity
Original:  Our algorithm can learn  SPARQL BGP queriescommon to a list of source-target-pairs from a given SPARQL endpoint.
Revised:  Our algorithm can learn patterns (SPARQL queries) from a SPARQL BGP queriescommon to a list of source-target-pairs from a given SPARQL endpoint.
Edit intent: clarity
Original:  Our algorithm can learn  SPARQL BGP queriescommon to a list of source-target-pairs from a given SPARQL endpoint.
Revised:  Our algorithm can learn SPARQL endpoint.
Edit intent: clarity
Original:  Further, we use the resulting SPARQL queries to mimic human associations with a  Recall@10 > 63.9 \%.
Revised:  Further, we use the resulting SPARQL queries to mimic human associations with a Recall@10 of 63.9 \%.
Edit intent: clarity
Original: We study various kinds of line segments covering problems with axis-parallel unit squares in two dimensions .
Revised: We study several variations of line segment covering problem with axis-parallel unit squares in two dimensions .
Edit intent: clarity
Original:  We may have different variations of this problem depending on the orientation and length of the input segments.
Revised:  The variations depend on the orientation and length of the input segments.
Edit intent: clarity
Original:   Further, we show that our problems have connections with the problems studied by Arkin et al. ( 2015 ) on conflict-free covering problem.
Revised:  Further, we show that our problems have connections with the problems studied by Arkin et al. 2015 ) on conflict-free covering problem.
Edit intent: fluency
Original:   Further, we show that our problems have connections with the problems studied by Arkin et al. ( 2015 ) on conflict-free covering problem.
Revised:  Further, we show that our problems have connections with the problems studied by Arkin et al. ( 2015 on conflict-free covering problem.
Edit intent: fluency