wanyu/IteraTeR_v2 huggingface dataset:
Original:  The results show that the proposed low complexity interference coordination schemes achieve high spectral efficiency and good scalability while assuring low outage probability to provide QoS for all users.
Revised:  The results show that the proposed low complexity interference coordination schemes achieve high spectral efficiency and good scalability while assuring low outage probability can be assured to provided QoS for all users.
Edit intent: clarity
Original:  The Firedrake/PyOP2 code is inherently parallel and we present a detailled performance analysis for a single node (24 cores) on the ARCHER supercomputer.
Revised:  The Firedrake/PyOP2 code is inherently parallel and we present a detailed performance analysis for a single node (24 cores) on the ARCHER supercomputer.
Edit intent: fluency
Original:  Specifically, we use persistent homology in combination with a weight rank clique filtration to gain insights into these functional networks, and we use persistence landscapes to interpret our results.
Revised:  We use persistent homology in combination with a weight rank clique filtration to gain insights into these functional networks, and we use persistence landscapes to interpret our results.
Edit intent: coherence
Original:  With these examples, we demonstrate that (1) using persistent homology to study functional networks provides fascinating insights into their properties and (2) the position of the features in a filtration can play a more vital role than persistence in the interpretation of topological features, even though  the latter is used more commonly to distinguish between signal and noise.
Revised:  With these examples, we demonstrate that (1) using persistent homology to study functional networks provides fascinating insights into their properties and (2) the position of the features in a filtration can play a more vital role than persistence in the interpretation of topological features, even though conventionally the latter is used more commonly to distinguish between signal and noise.
Edit intent: coherence
Original:  With these examples, we demonstrate that (1) using persistent homology to study functional networks provides fascinating insights into their properties and (2) the position of the features in a filtration can play a more vital role than persistence in the interpretation of topological features, even though  the latter is used more commonly to distinguish between signal and noise.
Revised:  With these examples, we demonstrate that (1) using persistent homology to study functional networks provides fascinating insights into their properties and (2) the position of the features in a filtration can play a more vital role than persistence in the interpretation of topological features, even though the latter is used to distinguish between signal and noise.
Edit intent: clarity
Original:  We find that in particular, persistent homology can detect differences in synchronisation patterns in our data sets over time giving insight on changes in community structure in the networks , and on increased synchronisation between brain regions forming loops in the functional network during motor-learning .
Revised:  We find that persistent homology can detect differences in synchronisation patterns in our data sets over time giving insight on changes in community structure in the networks , and on increased synchronisation between brain regions forming loops in the functional network during motor-learning .
Edit intent: coherence
Original:  We find that in particular, persistent homology can detect differences in synchronisation patterns in our data sets over time giving insight on changes in community structure in the networks , and on increased synchronisation between brain regions forming loops in the functional network during motor-learning .
Revised:  We find that in particular, persistent homology can detect differences in synchronization patterns in our data sets over time giving insight on changes in community structure in the networks , and on increased synchronisation between brain regions forming loops in the functional network during motor-learning .
Edit intent: fluency
Original:  We find that in particular, persistent homology can detect differences in synchronisation patterns in our data sets over time giving insight on changes in community structure in the networks , and on increased synchronisation between brain regions forming loops in the functional network during motor-learning .
Revised:  We find that in particular, persistent homology can detect differences in synchronisation patterns in our data sets over time , giving insight both on changes in community structure in the networks , and on increased synchronisation between brain regions forming loops in the functional network during motor-learning .
Edit intent: clarity
Original:  We find that in particular, persistent homology can detect differences in synchronisation patterns in our data sets over time giving insight on changes in community structure in the networks , and on increased synchronisation between brain regions forming loops in the functional network during motor-learning .
Revised:  We find that in particular, persistent homology can detect differences in synchronisation patterns in our data sets over time giving insight on changes in community structure in the networks and on increased synchronisation between brain regions forming loops in the functional network during motor-learning .
Edit intent: fluency
Original:  We find that in particular, persistent homology can detect differences in synchronisation patterns in our data sets over time giving insight on changes in community structure in the networks , and on increased synchronisation between brain regions forming loops in the functional network during motor-learning .
Revised:  We find that in particular, persistent homology can detect differences in synchronisation patterns in our data sets over time giving insight on changes in community structure in the networks , and on increased synchronization between brain regions forming loops in the functional network during motor-learning .
Edit intent: fluency
Original:  We find that in particular, persistent homology can detect differences in synchronisation patterns in our data sets over time giving insight on changes in community structure in the networks , and on increased synchronisation between brain regions forming loops in the functional network during motor-learning .
Revised:  We find that in particular, persistent homology can detect differences in synchronisation patterns in our data sets over time giving insight on changes in community structure in the networks , and on increased synchronisation between brain regions that form loops in a functional network during motor-learning .
Edit intent: clarity
Original:  We find that in particular, persistent homology can detect differences in synchronisation patterns in our data sets over time giving insight on changes in community structure in the networks , and on increased synchronisation between brain regions forming loops in the functional network during motor-learning .
Revised:  We find that in particular, persistent homology can detect differences in synchronisation patterns in our data sets over time giving insight on changes in community structure in the networks , and on increased synchronisation between brain regions forming loops in the functional network during motor learning .
Edit intent: fluency
Original:  For the motor-learning data we also observe that persistence landscapes reveal that the majority of changes in the loops of the network takes place on the second of three days of the learning process.
Revised:  For the motor-learning data , persistence landscapes also reveal that on average the majority of changes in the loops of the network takes place on the second of three days of the learning process.
Edit intent: clarity
Original:  For the motor-learning data we also observe that persistence landscapes reveal that the majority of changes in the loops of the network takes place on the second of three days of the learning process.
Revised:  For the motor-learning data we also observe that persistence landscapes reveal that the majority of changes in the network loops takes place on the second of three days of the learning process.
Edit intent: clarity
Original:  We use persistent homology in combination with a weight rank clique filtration to gain insights into these functional networks, and we use persistence landscapes to interpret our results.
Revised:  We use persistent homology with a weight rank clique filtration to gain insights into these functional networks, and we use persistence landscapes to interpret our results.
Edit intent: clarity
Original:  With these examples, we demonstrate that (1) using persistent homology to study functional networks provides fascinating insights into their properties and (2) the position of the features in a filtration can  play a more vital role than persistence in the interpretation of topological features, even though conventionally the latter is used to distinguish between signal and noise.
Revised:  With these examples, we demonstrate that (1) using persistent homology to study functional networks provides fascinating insights into their properties and (2) the position of the features in a filtration can sometimes play a more vital role than persistence in the interpretation of topological features, even though conventionally the latter is used to distinguish between signal and noise.
Edit intent: coherence
Original:  For the motor-learning data, persistence landscapes also reveal that on average the majority of changes in the network loops takes place on the second of  three days of the learning process.
Revised:  For the motor-learning data, persistence landscapes also reveal that on average the majority of changes in the network loops take place on the second of three days of the learning process.
Edit intent: fluency
Original:  For the motor-learning data, persistence landscapes also reveal that on average the majority of changes in the network loops takes place on the second of  three days of the learning process.
Revised:  For the motor-learning data, persistence landscapes also reveal that on average the majority of changes in the network loops takes place on the second of the three days of the learning process.
Edit intent: fluency
Original:  The association strength at a given training trial corresponds to a point in a disconnected set at a given iteration level.
Revised:  The association strength at a training trial corresponds to a point in a disconnected set at a given iteration level.
Edit intent: fluency
Original:  In particular, the dimension of fractals is a parameter that can both measure the efficiency of a given conditioning model (in terms of the salience of the stimuli for the experimental subject) and compare the efficiency of different models.
Revised:  In particular, the dimension of fractals can measure the efficiency of a given conditioning model (in terms of the salience of the stimuli for the experimental subject) and compare the efficiency of different models.
Edit intent: clarity
Original:  In particular, the dimension of fractals is a parameter that can both measure the efficiency of a given conditioning model (in terms of the salience of the stimuli for the experimental subject) and compare the efficiency of different models.
Revised:  In particular, the dimension of fractals is a parameter that can both measure the efficiency of conditioning models.
Edit intent: coherence
Original: Several ' edge-discovery' applications over graph-based data models are known to have worst-case quadratic complexity , even if the discovered edges are sparse.
Revised: Several ` edge-discovery' applications over graph-based data models are known to have worst-case quadratic complexity , even if the discovered edges are sparse.
Edit intent: fluency
Original:  With such a development, the complexity-reducing scope of DNF schemes becomes applicable to a variety of problems, including entity resolution and type alignment between heterogeneous RDF graphs, and link prediction in networks represented as attributed graphs.
Revised:  With such a development, the complexity-reducing scope of DNF schemes becomes applicable to a variety of problems, including entity resolution and type alignment between heterogeneous graphs, and link prediction in networks represented as attributed graphs.
Edit intent: clarity
Original:  The evolutionary dynamics that led to these broken symmetries remain unknown.
Revised:  The evolutionary advantages of these broken symmetries remain unknown.
Edit intent: clarity
Original:  Our model results and  explanations are consistent with multiple lines of experimental evidence, which include evidence for the presence of asymmetric cooperativity in DNA.
Revised:  Our model results and tentative explanations are consistent with multiple lines of experimental evidence, which include evidence for the presence of asymmetric cooperativity in DNA.
Edit intent: clarity
Original: For the case that the numbers of annual published papers in some citation networks grow linearly , a geometric model is  proposed to predict some statistical features of those networks, in which the academic influence scopes of  papers are denoted through specific geometric areas related to time and space.
Revised: Due to the fact that the numbers of annual published papers in some citation networks grow linearly , a geometric model is proposed to predict some statistical features of those networks, in which the academic influence scopes of papers are denoted through specific geometric areas related to time and space.
Edit intent: coherence
Original: For the case that the numbers of annual published papers in some citation networks grow linearly , a geometric model is  proposed to predict some statistical features of those networks, in which the academic influence scopes of  papers are denoted through specific geometric areas related to time and space.
Revised: For the case that the numbers of annually published papers have witnessed a linear growth in some citation networks grow linearly , a geometric model is proposed to predict some statistical features of those networks, in which the academic influence scopes of papers are denoted through specific geometric areas related to time and space.
Edit intent: clarity
Original: For the case that the numbers of annual published papers in some citation networks grow linearly , a geometric model is  proposed to predict some statistical features of those networks, in which the academic influence scopes of  papers are denoted through specific geometric areas related to time and space.
Revised: For the case that the numbers of annual published papers in some citation networks , a geometric model is proposed to predict some statistical features of those networks, in which the academic influence scopes of papers are denoted through specific geometric areas related to time and space.
Edit intent: clarity
Original: For the case that the numbers of annual published papers in some citation networks grow linearly , a geometric model is  proposed to predict some statistical features of those networks, in which the academic influence scopes of  papers are denoted through specific geometric areas related to time and space.
Revised: For the case that the numbers of annual published papers in some citation networks grow linearly , a geometric model is thus proposed to predict some statistical features of those networks, in which the academic influence scopes of papers are denoted through specific geometric areas related to time and space.
Edit intent: coherence
Original: For the case that the numbers of annual published papers in some citation networks grow linearly , a geometric model is  proposed to predict some statistical features of those networks, in which the academic influence scopes of  papers are denoted through specific geometric areas related to time and space.
Revised: For the case that the numbers of annual published papers in some citation networks grow linearly , a geometric model is proposed to predict some statistical features of those networks, in which the academic influence scopes of the papers are denoted through specific geometric areas related to time and space.
Edit intent: fluency
Original:  Edges (citations) are linked according to an influence mechanism which indicates  an existing paper will be cited by a new paper locating in its influence zone.
Revised:  Edges (citations) are linked according to an influence mechanism which indicates that an existing paper will be cited by a new paper locating in its influence zone.
Edit intent: fluency
Original:  Edges (citations) are linked according to an influence mechanism which indicates  an existing paper will be cited by a new paper locating in its influence zone.
Revised:  Edges (citations) are linked according to an influence mechanism which indicates an existing paper will be cited by a new paper located in its influence zone.
Edit intent: fluency
Original:  Considering the citations between papers in different disciplines, an interdisciplinary citation mechanism is added into the model in which some papers chosen with a small probability  will cite some existing papers randomly and uniformly.
Revised:  Considering the citations among papers in different disciplines, an interdisciplinary citation mechanism is added into the model in which some papers chosen with a small probability will cite some existing papers randomly and uniformly.
Edit intent: fluency
Original:  Considering the citations between papers in different disciplines, an interdisciplinary citation mechanism is added into the model in which some papers chosen with a small probability  will cite some existing papers randomly and uniformly.
Revised:  Considering the citations between papers in different disciplines, an interdisciplinary citation mechanism is added to the model in which some papers chosen with a small probability will cite some existing papers randomly and uniformly.
Edit intent: fluency
Original:  Considering the citations between papers in different disciplines, an interdisciplinary citation mechanism is added into the model in which some papers chosen with a small probability  will cite some existing papers randomly and uniformly.
Revised:  Considering the citations between papers in different disciplines, an interdisciplinary citation mechanism is added into the model in which some papers with a small probability will cite some existing papers randomly and uniformly.
Edit intent: clarity
Original:  Considering the citations between papers in different disciplines, an interdisciplinary citation mechanism is added into the model in which some papers chosen with a small probability  will cite some existing papers randomly and uniformly.
Revised:  Considering the citations between papers in different disciplines, an interdisciplinary citation mechanism is added into the model in which some papers chosen with a small probability of being chosen will cite some existing papers randomly and uniformly.
Edit intent: clarity
Original:  Different from most existing models which only study the scale-free tail of the in-degree distribution, this model characterize the overall in-degree distribution well .
Revised:  Different from most existing models that only study the scale-free tail of the in-degree distribution, this model characterize the overall in-degree distribution well .
Edit intent: fluency
Original:  Different from most existing models which only study the scale-free tail of the in-degree distribution, this model characterize the overall in-degree distribution well .
Revised:  Different from most existing models which only study the scale-free tail of the in-degree distribution, this model also characterizes the overall in-degree distribution well .
Edit intent: clarity
Original:  Different from most existing models which only study the scale-free tail of the in-degree distribution, this model characterize the overall in-degree distribution well .
Revised:  Different from most existing models which only study the scale-free tail of the in-degree distribution, this model characterize the overall in-degree distribution .
Edit intent: clarity
Original:  Moreover, it describes some other important statistical characteristics of real networks, such as in- and out-assortativity, giant component and clear community structure.
Revised:  Moreover, it presents the description of some other important statistical characteristics of real networks, such as in- and out-assortativity, giant component and clear community structure.
Edit intent: clarity
Original: A Pythagorean triple is a triple of positive integers a, b, c \in N- { 0 } satisfying a ^2 + b ^2 = c ^2.
Revised: A Pythagorean triple is a triple of positive integers a, b, c \in N { 0 } satisfying a ^2 + b ^2 = c ^2.
Edit intent: clarity
Original: A Pythagorean triple is a triple of positive integers a, b, c \in N- { 0 } satisfying a ^2 + b ^2 = c ^2.
Revised: A Pythagorean triple is a triple of positive integers a, b, c \in N- { } satisfying a ^2 + b ^2 = c ^2.
Edit intent: clarity
Original: A Pythagorean triple is a triple of positive integers a, b, c \in N- { 0 } satisfying a ^2 + b ^2 = c ^2.
Revised: A Pythagorean triple is a triple of positive integers a, b, c \in N- { 0 } ^{+ ^2 + b ^2 = c ^2.
Edit intent: clarity
Original:  In other words, is the Diophantine equation X ^2+ Y ^2 = Z ^2 regular?
Revised:  In other words, is the Dio-phantine equation X ^2+ Y ^2 = Z ^2 regular?
Edit intent: fluency
Original:  This problem has been open since several decades, even restricted to 2-colorings .
Revised:  This problem , recently solved for 2-colorings .
Edit intent: coherence
Original:  In this note  ,  \ge  we introduce partial morphisms , which are special colorings of N- 0%DIFDELCMD < } %%% by finite groups with partly multiplicative properties.
Revised:  In this note , \ge we introduce partial morphisms , which are special colorings of N- 0%DIFDELCMD < } %%% in finite groups with partly multiplicative properties.
Edit intent: clarity
Original:  We show that, for many such colorings , monochromatic Pythagorean triples are impossible to avoid in the integer interval 1, 10000 .
Revised:  We show that, for many such colorings , monochromatic Pythagorean triples are 1, 10000 .
Edit intent: clarity
Original: Given a random n-variate degree-d homogeneous polynomial f, we study the following problem:%DIFDELCMD < \[ \| x \| = 1 f(x).
Revised: For an n-variate degree-d homogeneous polynomial f, we study the following problem:%DIFDELCMD < \[ \| x \| = 1 f(x).
Edit intent: clarity
Original: Given a random n-variate degree-d homogeneous polynomial f, we study the following problem:%DIFDELCMD < \[ \| x \| = 1 f(x).
Revised: Given a random n-variate %DIFDELCMD < \[ \| x \| = 1 f(x).
Edit intent: coherence
Original:  We study the problem of efficiently certifying upper bounds on A_{\max} via the natural relaxation from the } Sum of Squares (SoS) hierarchy performs on this problem .
Revised:  We study the problem of efficiently certifying upper bounds on A_{\max} via the natural relaxation from the } Sum of Squares (SoS) hierarchy .
Edit intent: clarity
Original:  When f is a degree-q polynomial with independent random coefficients , we prove that there is a constant c such that with high probability, degree-q SoS satisfies%DIFDELCMD < \[ %DIFDELCMD < (n{q^{\,\,c+o(1)}})^{q/4} \leq SoS-Value \leq %DIFDELCMD < (n{q^{\,\,c-o(1)}})^{q/4}. \]%%%  that satisfies }\[ B ~~~~\leq~~ A_{\max} \cdot \biggl(n{q^{\,1-o(1)}}\biggr)^{q/4-1/2} \quad w.h.p. \] Our upper bound improves a result of Montanari and Richard ~\mbox{ MR14\hspace{0pt} }  when q is large.
Revised:  When f is a degree-q polynomial with independent random coefficients , we prove that %DIFDELCMD < \[ %DIFDELCMD < (n{q^{\,\,c+o(1)}})^{q/4} \leq SoS-Value \leq %DIFDELCMD < (n{q^{\,\,c-o(1)}})^{q/4}. \]%%% that satisfies }\[ B ~~~~\leq~~ A_{\max} \cdot \biggl(n{q^{\,1-o(1)}}\biggr)^{q/4-1/2} \quad w.h.p. \] Our upper bound improves a result of Montanari and Richard ~\mbox{ MR14\hspace{0pt} } when q is large.
Edit intent: clarity