wanyu/IteraTeR_v2 huggingface dataset:
Original:  Specifically , given an SDP with m constraint matrices, each of dimension n and rank \mathrm{poly(\log n)}  , our algorithm gives a succinct description and any entry of the solution matrix in time O(m\cdotpoly(\log n,  1/\varepsilon)) given access to a sample-based low-overhead data structure of the constraint matrices, where \varepsilon is the precision of the solution.
Revised:  Specifically , given an SDP with m constraint matrices, each of dimension n and rank (\log n)} , our algorithm gives a succinct description and any entry of the solution matrix in time O(m\cdotpoly(\log n, 1/\varepsilon)) given access to a sample-based low-overhead data structure of the constraint matrices, where \varepsilon is the precision of the solution.
Edit intent: clarity
Original:  Specifically , given an SDP with m constraint matrices, each of dimension n and rank \mathrm{poly(\log n)}  , our algorithm gives a succinct description and any entry of the solution matrix in time O(m\cdotpoly(\log n,  1/\varepsilon)) given access to a sample-based low-overhead data structure of the constraint matrices, where \varepsilon is the precision of the solution.
Revised:  Specifically , given an SDP with m constraint matrices, each of dimension n and rank \mathrm{poly(\log n)} r , our algorithm gives a succinct description and any entry of the solution matrix in time O(m\cdotpoly(\log n, 1/\varepsilon)) given access to a sample-based low-overhead data structure of the constraint matrices, where \varepsilon is the precision of the solution.
Edit intent: clarity
Original:  Specifically , given an SDP with m constraint matrices, each of dimension n and rank \mathrm{poly(\log n)}  , our algorithm gives a succinct description and any entry of the solution matrix in time O(m\cdotpoly(\log n,  1/\varepsilon)) given access to a sample-based low-overhead data structure of the constraint matrices, where \varepsilon is the precision of the solution.
Revised:  Specifically , given an SDP with m constraint matrices, each of dimension n and rank \mathrm{poly(\log n)} , our algorithm gives a succinct description and any entry of the solution matrix in time O(m\cdotpoly(\log n, 1/\varepsilon)) given access to a sampling-based low-overhead data structure of the constraint matrices, where \varepsilon is the precision of the solution.
Edit intent: fluency
Original:  Specifically , given an SDP with m constraint matrices, each of dimension n and rank \mathrm{poly(\log n)}  , our algorithm gives a succinct description and any entry of the solution matrix in time O(m\cdotpoly(\log n,  1/\varepsilon)) given access to a sample-based low-overhead data structure of the constraint matrices, where \varepsilon is the precision of the solution.
Revised:  Specifically , given an SDP with m constraint matrices, each of dimension n and rank \mathrm{poly(\log n)} , our algorithm gives a succinct description and any entry of the solution matrix in time O(m\cdotpoly(\log n, 1/\varepsilon)) given access to a sample-based low-overhead data structure for the constraint matrices, where \varepsilon is the precision of the solution.
Edit intent: fluency
Original:  \bullet Symmetric approximation: we propose a sampling procedure that gives \emph{  low-rank spectral decomposition of a Hermitian matrix A.
Revised:  \bullet Symmetric approximation: we propose a sampling procedure that gives the\emph{ low-rank spectral decomposition of a Hermitian matrix A.
Edit intent: fluency
Original:  \bullet Symmetric approximation: we propose a sampling procedure that gives \emph{  low-rank spectral decomposition of a Hermitian matrix A.
Revised:  \bullet Symmetric approximation: we propose a sampling procedure that gives \emph{ of a low-rank spectral decomposition of a Hermitian matrix A.
Edit intent: clarity
Original:  \bullet Symmetric approximation: we propose a sampling procedure that gives \emph{  low-rank spectral decomposition of a Hermitian matrix A.
Revised:  \bullet Symmetric approximation: we propose a sampling procedure that gives \emph{ low-rank Hermitian matrix A.
Edit intent: clarity
Original:  This improves upon previous sampling procedures that only give low-rank singular value decompositions, losing the signs of eigenvalues .
Revised:  To the best of our knowledge, this is the first sampling-based algorithm for spectral decomposition, as previous works only give singular values and vectors .
Edit intent: clarity
Original: In this article, we perform a parameter study for a recently developed model in karst hydrology .
Revised: In this article, we perform a parameter study for a recently developed karst hydrological model .
Edit intent: clarity
Original:  For the first time in karst hydrology . we use the active subspace method to find directions in the parameter space that drive the update from the prior to the posterior distribution in order to effectively reduce the dimension of the problem and for computational efficiency.
Revised:  For the first time in karst hydrology , we use the active subspace method to find directions in the parameter space that drive the update from the prior to the posterior distribution in order to effectively reduce the dimension of the problem and for computational efficiency.
Edit intent: fluency
Original:  We show that this particular real world scenario has implicit low-dimensionality, and we run an adjusted Markov chain Monte Carlo algorithm in a low-dimensional subspace to construct samples of the posterior distribution.
Revised:  We show that this case study has implicit low-dimensionality, and we run an adjusted Markov chain Monte Carlo algorithm in a low-dimensional subspace to construct samples of the posterior distribution.
Edit intent: clarity
Original: Real datasets often come in the form of an unorganised cloud of points .
Revised: Real datasets often come in the form of a cloud of points .
Edit intent: clarity
Original:  The skeletonisation problem for a point cloud is to find a graph or a skeleton that correctly represents the shape of a cloud.
Revised:  The skeletonisation problem for a point cloud is to find a graph or a skeleton that correctly represents a shape of the cloud.
Edit intent: fluency
Original:  HoPeS represents the 1-dimensional shape of a cloud at any scale by the Optimality Theorem.
Revised:  HoPeS represents the 1-dimensional shape of the cloud at any scale by the Optimality Theorem.
Edit intent: fluency
Original:  The  experiments on synthetic and real data show that HoPeS outperforms the other algorithms on several topological and geometric measures .
Revised:  The extensive experiments on synthetic and real data show that HoPeS outperforms the other algorithms on several topological and geometric measures .
Edit intent: clarity
Original:  In this paper, we propose a neural network based model that segments symbols into stroke level components.
Revised:  In this paper, we propose a neural network model that segments symbols into stroke level components.
Edit intent: coherence
Original:  In this paper, we propose a neural network based model that segments symbols into stroke level components.
Revised:  In this paper, we propose a neural network based model that segments symbols into stroke-level components.
Edit intent: fluency
Original:  Our segmentation network has two main elements: a fixed feature extractor and a multilayer perceptron (MLP) network that identifies a component based on the feature.
Revised:  Our segmentation framework has two main elements: a fixed feature extractor and a multilayer perceptron (MLP) network that identifies a component based on the feature.
Edit intent: clarity
Original:  Our segmentation network has two main elements: a fixed feature extractor and a multilayer perceptron (MLP) network that identifies a component based on the feature.
Revised:  Our segmentation network has two main elements: a fixed feature extractor and a Multilayer Perceptron (MLP) network that identifies a component based on the feature.
Edit intent: fluency
Original:  As the feature extractor we utilize an encoder of the generative Variational Auto-Encoder (VAE) framework that draws symbols in stroke by stroke basis.
Revised:  As the feature extractor we utilize an encoder of the generative Variational Auto-Encoder (VAE) model that reconstructs symbols on a stroke by stroke basis.
Edit intent: clarity
Original:  Experiments show that a single encoder could be reused for segmenting multiple categories of sketches with negligible effects on segmentation accuracies.
Revised:  Experiments show that a single encoder could be reused for segmenting multiple categories of sketched symbols with negligible effects on segmentation accuracies.
Edit intent: clarity
Original:  Extensive evaluations on our newly annotated  dataset demonstrate that our model obtains significantly better scores as compared to the best baseline model.
Revised:  Extensive evaluations on our newly annotated dataset demonstrate that our framework obtains significantly better scores as compared to the best baseline model.
Edit intent: clarity
Original:  Extensive evaluations on our newly annotated  dataset demonstrate that our model obtains significantly better scores as compared to the best baseline model.
Revised:  Extensive evaluations on our newly annotated dataset demonstrate that our model obtains significantly better accuracies as compared to the best baseline model.
Edit intent: clarity
Original: We propose PiNcH, a methodology to detect the presence of a drone and its current status  leveraging just the communication traffic exchanged between the drone and its Remote Controller (RC).
Revised: We propose PiNcH, a methodology to detect the presence of a drone , its current status leveraging just the communication traffic exchanged between the drone and its Remote Controller (RC).
Edit intent: coherence
Original:  Indeed, it is fully passive and it resorts to cheap and general purpose hardware.
Revised:  Indeed, it is fully passive and it requires just cheap and general-purpose hardware.
Edit intent: clarity
Original:  To evaluate the effectiveness of our solution, we collected real communication measurements from the 3DR SOLO drone , being the most popular open-source hardware, running the widespread ArduCopter open-source firmware,  mounted on-board on a wide range  of commercial amateur drones.
Revised:  To evaluate the effectiveness of our solution, we collected real communication traces originated by a drone running the widespread ArduCopter open-source firmware, mounted on-board on a wide range of commercial amateur drones.
Edit intent: clarity
Original:  To evaluate the effectiveness of our solution, we collected real communication measurements from the 3DR SOLO drone , being the most popular open-source hardware, running the widespread ArduCopter open-source firmware,  mounted on-board on a wide range  of commercial amateur drones.
Revised:  To evaluate the effectiveness of our solution, we collected real communication measurements from the 3DR SOLO drone , being the most popular open-source hardware, running the widespread ArduCopter open-source firmware, currently mounted on-board on a wide range of commercial amateur drones.
Edit intent: clarity
Original:  To evaluate the effectiveness of our solution, we collected real communication measurements from the 3DR SOLO drone , being the most popular open-source hardware, running the widespread ArduCopter open-source firmware,  mounted on-board on a wide range  of commercial amateur drones.
Revised:  To evaluate the effectiveness of our solution, we collected real communication measurements from the 3DR SOLO drone , being the most popular open-source hardware, running the widespread ArduCopter open-source firmware, mounted on-board of a wide range of commercial amateur drones.
Edit intent: fluency
Original:  Then, we test our solution against different publicly available wireless traces.
Revised:  We tested our solution against different publicly available wireless traces.
Edit intent: coherence
Original:  (iii) discriminate the movement of the drone;
Revised:  (iii) discriminate the movements of the drone;
Edit intent: fluency
Original:  and, finally, (iv) estimate a lower bound on the time required to identify a drone with the requested level of assurance.
Revised:  and, finally, (iv) enjoy a reduced upper bound on the time required to identify a drone with the requested level of assurance.
Edit intent: clarity
Original:  The  quality and viability of our solution  do prove that network traffic analysis can be successfully adopted for drone identification and pave the way for future research in the area .
Revised:  The quality and viability of our solution , do prove that network traffic analysis can be successfully adopted for drone identification and pave the way for future research in the area .
Edit intent: fluency
Original:  The input is a graph G=(V,E) where the edge set E is partitioned into a set E _b of blue edges and a set E _r of red edges.
Revised:  The input is a graph G=(V,E) where the edge set E is partitioned into a set E _r of red edges and a set E _r of red edges.
Edit intent: fluency
Original:  Moreover, we provide a polynomial-time algorithm for the case if G contains no blue P_3, red P_3, blue K_3, and red K_3. Finally, we show that Bicolored P_3 Deletion can be solved in \mathcal{O ^k\cdot |V| ^5 ) time and that it admits a kernel with \mathcal{O(\Delta k^2}  ) vertices, where \Delta is the maximum degree of G.
Revised:  Moreover, we provide a polynomial-time algorithm for the case that G contains no blue P_3, red P_3, blue K_3, and red K_3. Finally, we show that Bicolored P_3 Deletion can be solved in \mathcal{O ^k\cdot |V| ^5 ) time and that it admits a kernel with \mathcal{O(\Delta k^2} ) vertices, where \Delta is the maximum degree of G.
Edit intent: fluency
Original:  Moreover, we provide a polynomial-time algorithm for the case if G contains no blue P_3, red P_3, blue K_3, and red K_3. Finally, we show that Bicolored P_3 Deletion can be solved in \mathcal{O ^k\cdot |V| ^5 ) time and that it admits a kernel with \mathcal{O(\Delta k^2}  ) vertices, where \Delta is the maximum degree of G.
Revised:  Moreover, we provide a polynomial-time algorithm for the case if G contains no blue P_3, red P_3, blue K_3, and red K_3. Finally, we show that Bicolored P_3 Deletion can be solved in \mathcal{O ^k\cdot |V| ^5 ) time and that it admits a kernel with (\Delta k^2} ) vertices, where \Delta is the maximum degree of G.
Edit intent: fluency
Original:  Mining 12 millions of Twitter messages, we reconstruct a network in which users interchange opinions related to the impeachment of  former Brazilian President Dilma Rousseff.
Revised:  Mining 12 million Twitter messages, we reconstruct a network in which users interchange opinions related to the impeachment of former Brazilian President Dilma Rousseff.
Edit intent: clarity
Original:  Mining 12 millions of Twitter messages, we reconstruct a network in which users interchange opinions related to the impeachment of  former Brazilian President Dilma Rousseff.
Revised:  Mining 12 millions of Twitter messages, we reconstruct a network in which users interchange opinions related to the impeachment of the former Brazilian President Dilma Rousseff.
Edit intent: fluency
Original:  We define a continuous polarization parameter  that allows to quantify the presence of echo chambers  , reflected in two  communities of similar size with opposite views of the impeachment process.
Revised:  We define a continuous political position that allows to quantify the presence of echo chambers , reflected in two communities of similar size with opposite views of the impeachment process.
Edit intent: clarity
Original:  We define a continuous polarization parameter  that allows to quantify the presence of echo chambers  , reflected in two  communities of similar size with opposite views of the impeachment process.
Revised:  We define a continuous polarization parameter that allows to quantify the presence of echo chambers , reflected in two communities of similar sizes with opposite views of the impeachment process.
Edit intent: fluency
Original:  By means of simple spreading models, we show that the capability of users in propagating the content they produce, measured by the associated spreadability, strongly depends on the their polarization .
Revised:  By means of simple spreading models, we show that the capability of users in propagating the content they produce, measured by the associated spreadability, strongly depends on their attitude .
Edit intent: clarity
Original:  Furthermore, the users' spreadability is strictly correlated to the diversity, in terms of political polarization , of the audience reached.
Revised:  Furthermore, the users' spreadability is correlated to the diversity, in terms of political polarization , of the audience reached.
Edit intent: clarity
Original:  Furthermore, the users' spreadability is strictly correlated to the diversity, in terms of political polarization , of the audience reached.
Revised:  Furthermore, the users' spreadability is strictly correlated to the diversity, in terms of political position , of the audience reached.
Edit intent: clarity
Original:  Perhaps more importantly, we obtain this by analyzing an extremely simple and natural algorithm.
Revised:  Perhaps more importantly, we obtain this by analyzing an extremely simple and well-known algorithm.
Edit intent: clarity
Original: The study of graph problems in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs.
Revised: The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs.
Edit intent: clarity
Original:  STOC'18%DIFDELCMD < ]%%% , Assadi et al.
Revised:  %DIFDELCMD < ]%%% , Assadi et al.
Edit intent: coherence
Original:  STOC'18%DIFDELCMD < ]%%% , Assadi et al.
Revised:  STOC'18%DIFDELCMD < ]%%% 
Edit intent: coherence
Original:  SODA'19%DIFDELCMD < ]%%% , and Ghaffari et al.
Revised:  %DIFDELCMD < ]%%% , and Ghaffari et al.
Edit intent: coherence
Original:  SODA'19%DIFDELCMD < ]%%% , and Ghaffari et al.
Revised:  SODA'19%DIFDELCMD < ]%%% 
Edit intent: coherence
Original:  PODC'18%DIFDELCMD < ]%%% , gave algorithms for finding a 1+\varepsilon approximate maximum matching in O(\log \log n) rounds using (n) memory per machine.
Revised:  %DIFDELCMD < ]%%% , gave algorithms for finding a 1+\varepsilon approximate maximum matching in O(\log \log n) rounds using (n) memory per machine.
Edit intent: coherence
Original:  PODC'18%DIFDELCMD < ]%%% , gave algorithms for finding a 1+\varepsilon approximate maximum matching in O(\log \log n) rounds using (n) memory per machine.
Revised:  PODC'18%DIFDELCMD < ]%%% (n) memory per machine.
Edit intent: coherence
Original:  PODC'18%DIFDELCMD < ]%%% , gave algorithms for finding a 1+\varepsilon approximate maximum matching in O(\log \log n) rounds using (n) memory per machine.
Revised:  PODC'18%DIFDELCMD < ]%%% , gave algorithms for finding a 1+\varepsilon approximate maximum matching in O(\log \log n) rounds using 
Edit intent: clarity
Original:  Despite this progress,  we still have a far more limited understanding of the central symmetry-breaking problem of maximal matching.
Revised:  Despite this progress, however, we still have a far more limited understanding of the central symmetry-breaking problem of maximal matching.
Edit intent: coherence
Original:  SPAA'11%DIFDELCMD < ] %%% which undesirably requires a strictly super-linear space of n^{1+\Omega(1)} per machine.
Revised:  %DIFDELCMD < ] %%% which undesirably requires a strictly super-linear space of n^{1+\Omega(1)} per machine.
Edit intent: coherence
Original:  SPAA'11%DIFDELCMD < ] %%% which undesirably requires a strictly super-linear space of n^{1+\Omega(1)} per machine.
Revised:  SPAA'11%DIFDELCMD < ] %%% , or require a strictly super-linear space of n^{1+\Omega(1)} per machine.
Edit intent: coherence
Original:  The algorithm edge-samples the graph,  partitions the vertices at random , and finds a  greedy maximal matching within each partition.
Revised:  The algorithm edge-samples the graph, randomly partitions the vertices at random , and finds a greedy maximal matching within each partition.
Edit intent: coherence
Original:  The algorithm edge-samples the graph,  partitions the vertices at random , and finds a  greedy maximal matching within each partition.
Revised:  The algorithm edge-samples the graph, partitions the vertices , and finds a greedy maximal matching within each partition.
Edit intent: clarity
Original:  The space can be further improved to mildly sublinear in n by standard techniques .
Revised:  The space can be further improved to mildly sublinear in n using standard techniques) .
Edit intent: fluency
Original:  As an immediate corollary, we get a 2 approximation for minimum vertex cover in essentially the same rounds and space.
Revised:  As an immediate corollary, we get a 2 approximate minimum vertex cover in essentially the same rounds and space.
Edit intent: fluency
Original:  Other corollaries include more efficient algorithms for 1 + \varepsilon approximate matching and 2 + \varepsilon approximate weighted matching .
Revised:  Other corollaries include more efficient algorithms for 1 + \varepsilon approximate matching .
Edit intent: clarity
Original:  All these results can also be implemented in the congested clique model within O(\log \log \Delta) rounds.
Revised:  All these results can also be implemented in the congested clique model within the same number of rounds.
Edit intent: clarity
Original:  In particular, Evolutionary Computation is in a unique position to take advantage of that power, and become the next deep learning  .
Revised:  In particular, Evolutionary Computation is in a unique position to take advantage of that power, and become the next deep learning " .
Edit intent: fluency
Original:  The weak point of all known approximation by juntas results is that they work in the range n>Ck, where C is an extremely fast growing function of the input parameters, such as the quality of approximation or the number of families we simultaneously approximate.
Revised:  The weak point of all known approximation by juntas results is that they work in the range n>Ck, where C is an extremely fast-growing function of the input parameters, such as the quality of approximation or the number of families we simultaneously approximate.
Edit intent: fluency
Original:  \% (e.g, for junta-type results for t-intersecting families or for families with no s-matching C is at least exponential in t or s).
Edit intent: coherence
Original:  For many extremal set theory problems, including the Erd \H os Matching Conjecture, or the Complete t-Intersection Theorem, it is sufficient to deal with shifted families only.
Revised:  For many extremal set theory problems, including the Erd \H{o Matching Conjecture, or the Complete t-Intersection Theorem, it is sufficient to deal with shifted families only.
Edit intent: fluency
Original:  The weak point of all known approximation by juntas results is that they work in the range n>Ck, where C is an extremely fast-growing function of the input parameters, such as the quality of approximation or the number of families we simultaneously approximate.
Revised:  The weak point of all known junta approximation results is that they work in the range n>Ck, where C is an extremely fast-growing function of the input parameters, such as the quality of approximation or the number of families we simultaneously approximate.
Edit intent: clarity
Original:  The weak point of all known approximation by juntas results is that they work in the range n>Ck, where C is an extremely fast-growing function of the input parameters, such as the quality of approximation or the number of families we simultaneously approximate.
Revised:  The weak point of all known approximation by juntas results is that they work in the range n>Ck, where C is an extremely fast growing function of the input parameters, such as the quality of approximation or the number of families we simultaneously approximate.
Edit intent: fluency