wanyu/IteraTeR_v2 huggingface dataset:
Original:  Our results demonstrate the suitabilty of Ising and Ising-like models for reading out, or decoding , spatial patterns of activity in large neural ensembles .
Revised:  Our results demonstrate the practicality of using the Ising model to read out, or decoding , spatial patterns of activity in large neural ensembles .
Edit intent: clarity
Original:  Our results demonstrate the suitabilty of Ising and Ising-like models for reading out, or decoding , spatial patterns of activity in large neural ensembles .
Revised:  Our results demonstrate the suitabilty of Ising and Ising-like models for reading out, or decode , spatial patterns of activity in large neural ensembles .
Edit intent: fluency
Original:  Our results demonstrate the suitabilty of Ising and Ising-like models for reading out, or decoding , spatial patterns of activity in large neural ensembles .
Revised:  Our results demonstrate the suitabilty of Ising and Ising-like models for reading out, or decoding , spatial patterns of activity comprised of many hundreds of neurons .
Edit intent: clarity
Original: Recently, oscillatory dynamics of complex networks has  attracted great attention due to its new physics of pattern formation as well as its wide applications, particularly, in neural networks .
Revised: Oscillatory dynamics of complex networks has attracted great attention due to its new physics of pattern formation as well as its wide applications, particularly, in neural networks .
Edit intent: coherence
Original: Recently, oscillatory dynamics of complex networks has  attracted great attention due to its new physics of pattern formation as well as its wide applications, particularly, in neural networks .
Revised: Recently, oscillatory dynamics of complex networks has recently attracted great attention due to its new physics of pattern formation as well as its wide applications, particularly, in neural networks .
Edit intent: fluency
Original: Recently, oscillatory dynamics of complex networks has  attracted great attention due to its new physics of pattern formation as well as its wide applications, particularly, in neural networks .
Revised: Recently, oscillatory dynamics of complex networks has attracted great attention .
Edit intent: coherence
Original:  In this article we study pattern formation in oscillatory complex networks consisting of excitable nodes.
Revised:  In this paper we study pattern formation in oscillatory complex networks consisting of excitable nodes.
Edit intent: fluency
Original:  We find there exist few center nodes and small skeletons for most oscillations.
Revised:  We find that there exist a few center nodes and small skeletons for most oscillations.
Edit intent: fluency
Original:  Complicated and seemly random oscillatory patterns can be viewed as well-organized target waves propagating from the center nodes through the shortest paths, and the shortest loop passing both the center nodes and their drivers plays the role of oscillation source.
Revised:  Complicated and seemingly random oscillatory patterns can be viewed as well-organized target waves propagating from the center nodes through the shortest paths, and the shortest loop passing both the center nodes and their drivers plays the role of oscillation source.
Edit intent: fluency
Original:  Complicated and seemly random oscillatory patterns can be viewed as well-organized target waves propagating from the center nodes through the shortest paths, and the shortest loop passing both the center nodes and their drivers plays the role of oscillation source.
Revised:  Complicated and seemly random oscillatory patterns can be viewed as well-organized target waves propagating from center nodes along the shortest paths, and the shortest loop passing both the center nodes and their drivers plays the role of oscillation source.
Edit intent: clarity
Original:  Complicated and seemly random oscillatory patterns can be viewed as well-organized target waves propagating from the center nodes through the shortest paths, and the shortest loop passing both the center nodes and their drivers plays the role of oscillation source.
Revised:  Complicated and seemly random oscillatory patterns can be viewed as well-organized target waves propagating from the center nodes through the shortest paths, and the shortest loops passing through both the center nodes and their drivers plays the role of oscillation source.
Edit intent: fluency
Original:  Complicated and seemly random oscillatory patterns can be viewed as well-organized target waves propagating from the center nodes through the shortest paths, and the shortest loop passing both the center nodes and their drivers plays the role of oscillation source.
Revised:  Complicated and seemly random oscillatory patterns can be viewed as well-organized target waves propagating from the center nodes through the shortest paths, and the shortest loop passing both the center nodes and their driver nodes play the role of oscillation source.
Edit intent: clarity
Original:  Reading the simple skeletons we can understand and predict various essential properties of oscillations of the original networks and effectively control (suppress, create and modulate ) the network oscillations.
Revised:  Reading the simple skeletons we are able to understand and predict various essential properties of oscillations of the original networks and effectively control (suppress, create and modulate ) the network oscillations.
Edit intent: clarity
Original:  Reading the simple skeletons we can understand and predict various essential properties of oscillations of the original networks and effectively control (suppress, create and modulate ) the network oscillations.
Revised:  Reading the simple skeletons we can understand and predict various essential properties of the oscillations and effectively modulate the oscillations.
Edit intent: clarity
Original:  These ideas and methods will open a new insight into the pattern formation in complex networks, and provide useful tools for studying oscillations of neural networks.
Revised:  These methods and results will give insights into pattern formation in complex networks, and provide useful tools for studying oscillations of neural networks.
Edit intent: clarity
Original:  These ideas and methods will open a new insight into the pattern formation in complex networks, and provide useful tools for studying oscillations of neural networks.
Revised:  These ideas and methods will open a new insight into the pattern formation in complex networks, and provide suggestive ideas for studying and controlling oscillations in neural networks.
Edit intent: clarity
Original:  we exhibit a class of `cycles' } formed by unit distance edges that are forbidden in convex n-gons, (ii) prove that the maximum number of unit distances is at most n \log_2 n + 4n, thereby improving the best known result by a factor of 2\pi, and (iii) we show that if we only use these two properties then we will not be able to further improve this bound by more than a factor of four .
Revised:  we exhibit a class of `cycles' } formed by unit distances that are forbidden in convex n-gons, (ii) prove that the maximum number of unit distances is at most n \log_2 n + 4n, thereby improving the best known result by a factor of 2\pi, and (iii) we show that if we only use these two properties then we will not be able to further improve this bound by more than a factor of four .
Edit intent: clarity
Original:  The first is to study rigorously the transient behavior of some  P2P networks where information is replicated and disseminated according to an epidemic type dynamics.
Revised:  The first is to study rigorously the transient behavior of some peer-to-peer ( P2P networks where information is replicated and disseminated according to an epidemic type dynamics.
Edit intent: clarity
Original:  The first is to study rigorously the transient behavior of some  P2P networks where information is replicated and disseminated according to an epidemic type dynamics.
Revised:  The first is to study rigorously the transient behavior of some P2P ) networks whenever information is replicated and disseminated according to an epidemic type dynamics.
Edit intent: clarity
Original:  The first is to study rigorously the transient behavior of some  P2P networks where information is replicated and disseminated according to an epidemic type dynamics.
Revised:  The first is to study rigorously the transient behavior of some P2P networks where information is replicated and disseminated according to epidemic-like dynamics.
Edit intent: clarity
Original:  The second is to use the insight gained  in order to predict how efficient are measures taken against peer to peer networks.
Revised:  The second is to use the insight gained in order to predict how efficient are measures taken against P2P networks.
Edit intent: fluency
Original:  We first study a model which extends a classical epidemic model to characterize the peer to peer swarms in the presence of free riding peers.
Revised:  We first study a model which extends a classical epidemic model , and characterize the P2P swarm behavior in presence of free riding peers.
Edit intent: clarity
Original:  We then study a second model that a peer initiates a contact with another peer chosen randomly.
Revised:  We then study a second model in which a peer initiates a contact with another peer chosen randomly.
Edit intent: fluency
Original:  In both cases , the network is shown to have a phase transition : a small change in the parameters causes a large change in the behavior of the network.
Revised:  In both cases the network is shown to have a phase transition : a small change in the parameters causes a large change in the behavior of the network.
Edit intent: fluency
Original:  In both cases , the network is shown to have a phase transition : a small change in the parameters causes a large change in the behavior of the network.
Revised:  In both cases , the network is shown to exhibit phase transitions : a small change in the parameters causes a large change in the behavior of the network.
Edit intent: clarity
Original:  We show in particular how the phase transition affects measures that content provider networks may take against P2P networks that distribute non-authorized music or books, and what is the efficiency of counter-measures.
Revised:  We show , in particular, how phase transitions affect measures of content providers against P2P networks that distribute non-authorized music or books, and what is the efficiency of counter-measures.
Edit intent: clarity
Original:  The first is to study rigorously the transient behavior of some peer-to-peer ( P2P ) networks whenever information is replicated and disseminated according to epidemic-like dynamics.
Revised:  The first is to study rigorously the transient behavior of some P2P ) networks whenever information is replicated and disseminated according to epidemic-like dynamics.
Edit intent: clarity
Original:  The first is to study rigorously the transient behavior of some peer-to-peer ( P2P ) networks whenever information is replicated and disseminated according to epidemic-like dynamics.
Revised:  The first is to study rigorously the transient behavior of some peer-to-peer ( P2P networks whenever information is replicated and disseminated according to epidemic-like dynamics.
Edit intent: fluency
Original:  The second is to use the insight gained from the previous analysis in order to predict how efficient are measures taken against  P2P  networks.
Revised:  The second is to use the insight gained from the previous analysis in order to predict how efficient are measures taken against peer-to-peer ( P2P networks.
Edit intent: fluency
Original:  The second is to use the insight gained from the previous analysis in order to predict how efficient are measures taken against  P2P  networks.
Revised:  The second is to use the insight gained from the previous analysis in order to predict how efficient are measures taken against P2P ) networks.
Edit intent: fluency
Original:  We first introduce a stochastic model which extends a classical epidemic model , and characterize the P2P swarm behavior in presence of free riding peers.
Revised:  We first introduce a stochastic model which extends a classical epidemic model and characterize the P2P swarm behavior in presence of free riding peers.
Edit intent: fluency
Original:  In both cases the network is shown to exhibit phase transitions : a small change in the parameters causes a large change in the behavior of the network.
Revised:  In both cases the network is shown to exhibit a phase transition : a small change in the parameters causes a large change in the behavior of the network.
Edit intent: fluency
Original:  We show, in particular, how phase transitions affect measures of content providers against P2P networks that distribute non-authorized music or books, and what is the efficiency of counter-measures.
Revised:  We show, in particular, how the phase transition affects measures that content provider networks may take against P2P networks that distribute non-authorized music or books, and what is the efficiency of counter-measures.
Edit intent: clarity
Original:  Recently, Janson, and Shapira and Yuster independently proved the following result on quasi-randomness of graphs.
Revised:  Recently, Shapira and Yuster independently proved the following result on quasi-randomness of graphs.
Edit intent: coherence
Original:  Recently, Janson, and Shapira and Yuster independently proved the following result on quasi-randomness of graphs.
Revised:  Recently, Janson, and Shapira and Yuster proved the following result on quasi-randomness of graphs.
Edit intent: clarity
Original:  Let k \ge 2 be a fixed integer, \alpha_1, \ldots , \alpha_k be positive reals satisfying i \alpha_i = 1 and (\alpha_1, \ldots , \alpha_k) \neq (1/k, \ldots , 1/k), and G be a graph on n vertices.
Revised:  Let k \ge 2 be a fixed integer, \alpha_1, ... , \alpha_k be positive reals satisfying i \alpha_i = 1 and (\alpha_1, \ldots , \alpha_k) \neq (1/k, \ldots , 1/k), and G be a graph on n vertices.
Edit intent: coherence
Original:  Let k \ge 2 be a fixed integer, \alpha_1, \ldots , \alpha_k be positive reals satisfying i \alpha_i = 1 and (\alpha_1, \ldots , \alpha_k) \neq (1/k, \ldots , 1/k), and G be a graph on n vertices.
Revised:  Let k \ge 2 be a fixed integer, \alpha_1, \ldots , \alpha_k be positive reals satisfying i \alpha_i = 1 and (\alpha_1, \ldots , \alpha_k) \neq (1/k, ... , 1/k), and G be a graph on n vertices.
Edit intent: coherence
Original:  If for every partition of the vertices of G into sets V_1, \ldots , V_k of size \alpha_1 n, \ldots , \alpha_k n, the number of complete graphs on k vertices which have exactly one vertex in each of these sets is similar to what we would expect in a random graph, then the graph is quasi-random.
Revised:  If for every partition of the vertices of G into sets V_1, ... , V_k of size \alpha_1 n, \ldots , \alpha_k n, the number of complete graphs on k vertices which have exactly one vertex in each of these sets is similar to what we would expect in a random graph, then the graph is quasi-random.
Edit intent: coherence
Original:  If for every partition of the vertices of G into sets V_1, \ldots , V_k of size \alpha_1 n, \ldots , \alpha_k n, the number of complete graphs on k vertices which have exactly one vertex in each of these sets is similar to what we would expect in a random graph, then the graph is quasi-random.
Revised:  If for every partition of the vertices of G into sets V_1, \ldots , V_k of size \alpha_1 n, ... , \alpha_k n, the number of complete graphs on k vertices which have exactly one vertex in each of these sets is similar to what we would expect in a random graph, then the graph is quasi-random.
Edit intent: coherence
Original:  However, both of the approaches which used graph limits and hypergraphs did not provide enough information to make any conclusion for the case (1/k, \ldots , 1/k).
Revised:  However, both of the approaches which used graph limits and hypergraphs did not provide enough information to make any conclusion for the case (1/k, ... , 1/k).
Edit intent: clarity
Original:  In their work, Janson, and Shapira and Yuster independently asked whether this case also forces the graph to be quasi-random.
Revised:  In their work, Shapira and Yuster independently asked whether this case also forces the graph to be quasi-random.
Edit intent: coherence
Original:  In their work, Janson, and Shapira and Yuster independently asked whether this case also forces the graph to be quasi-random.
Revised:  In their work, Janson, and Shapira and Yuster asked whether this case also forces the graph to be quasi-random.
Edit intent: clarity
Original:   In this paper, we positively answer this question by proving that the case (1/k, \ldots , 1/k) implies the quasi-randomness of the graph as well.
Revised:  In this paper, we positively answer this question by proving that the case (1/k, ... , 1/k) implies the quasi-randomness of the graph as well.
Edit intent: coherence
Original:  However, the method of quasi-random hypergraphs they used did not provide enough information to make any conclusion for the case (1/k,..., 1/k)  . In their work, Shapira and Yuster asked whether this case also forces the graph to be quasi-random.
Revised:  However, the method of quasi-random hypergraphs they used did not provide enough information to resolve the case (1/k,..., 1/k) . In their work, Shapira and Yuster asked whether this case also forces the graph to be quasi-random.
Edit intent: clarity
Original:  However, the method of quasi-random hypergraphs they used did not provide enough information to make any conclusion for the case (1/k,..., 1/k)  . In their work, Shapira and Yuster asked whether this case also forces the graph to be quasi-random.
Revised:  However, the method of quasi-random hypergraphs they used did not provide enough information to make any conclusion for the case (1/k,..., 1/k) for graphs . In their work, Shapira and Yuster asked whether this case also forces the graph to be quasi-random.
Edit intent: clarity
Original:  In this paper, we positively answer this questionby proving that the case (1/k,..., 1/k) implies the quasi-randomness of the graph as well .
Revised:  In this paper, we positively answer their question .
Edit intent: coherence
Original: We investigate edge-intersection graphs of paths in the plane grid  regarding a parameter called the bend-number.
Revised: We investigate edge-intersection graphs of paths in the plane grid , regarding a parameter called the bend-number.
Edit intent: fluency
Original:  We  provide new upper and lower bounds of the bend-number of any given simple graph in terms of the coloring number, edge clique covers and the maximum degree.
Revised:  We provide new upper and lower bounds of the bend-number of graphs in terms of the coloring number, edge clique covers and the maximum degree.
Edit intent: clarity
Original: Given a set S of n points in the plane and a fixed angle 0 < omega < pi, we show how to find  all triangles of minimum area with  angle omega that enclose S in O(n log n) time.
Revised: Given a set S of n points in the plane and a fixed angle 0 < omega < pi, we show how to find in O(n log n) time all triangles of minimum area with angle omega that enclose S in O(n log n) time.
Edit intent: clarity
Original: The Shortest Path Reconfiguration problem is defined as follows: Given is a graph G with vertices s and t, and two shortest st-paths P and P' . The question is whether there exists a sequence of shortest st-paths that starts with P , ends with P' , such that subsequent paths differ in only one vertex.
Revised: The Shortest Path Reconfiguration problem has as input a graph G with vertices s and t, and two shortest st-paths P and P' . The question is whether there exists a sequence of shortest st-paths that starts with P , ends with P' , such that subsequent paths differ in only one vertex.
Edit intent: clarity
Original: We construct an equivariant blowup of the space of real symmetric matrices, with a natural stratification indexed by trees, which keep track of eigenvalue coincidences.
Revised: The orientable cover of the moduli space of real symmetric matrices, with a natural stratification indexed by trees, which keep track of eigenvalue coincidences.
Edit intent: clarity
Original:  We suggest, without much justification, that systems of oscillators parametrized by these spaces may provide useful models in genomics.
Revised:  We suggest, without much justification, that systems of oscillators parametrized by such objects may provide useful models in genomics.
Edit intent: clarity
Original:  Like other entities that reproduce and evolve, words rise or decline depending upon a complex interplay between fitness and environment . Using Internet discussion communities as model systems, we show that the word niche, defined as the extent of the word's association with specific people and topics, is a strong determinant of changes in word frequency.
Revised:  Like other entities that are reproduced and evolve, words rise or decline depending upon a complex interplay between fitness and environment . Using Internet discussion communities as model systems, we show that the word niche, defined as the extent of the word's association with specific people and topics, is a strong determinant of changes in word frequency.
Edit intent: clarity
Original:  Like other entities that reproduce and evolve, words rise or decline depending upon a complex interplay between fitness and environment . Using Internet discussion communities as model systems, we show that the word niche, defined as the extent of the word's association with specific people and topics, is a strong determinant of changes in word frequency.
Revised:  Like other entities that reproduce and evolve, words rise or decline depending upon a complex interplay between their intrinsic properties and the environments in which they function . Using Internet discussion communities as model systems, we show that the word niche, defined as the extent of the word's association with specific people and topics, is a strong determinant of changes in word frequency.
Edit intent: clarity
Original:  Previous , a posteriori, studies have indicated that word frequency  is a correlate of word success at historical time scales.
Revised:  Previous studies have already indicated that word frequency is a correlate of word success at historical time scales.
Edit intent: clarity
Original:  Our longitudinal analysis reveals that the word niche is far more important than word frequency in the dynamics of the entire vocabulary at shorter time scales, as the language adapts to new concepts and social groupings.
Revised:  Our analysis of changes in word frequencies over time reveals that the word niche is far more important than word frequency in the dynamics of the entire vocabulary at shorter time scales, as the language adapts to new concepts and social groupings.
Edit intent: clarity
Original:  Our longitudinal analysis reveals that the word niche is far more important than word frequency in the dynamics of the entire vocabulary at shorter time scales, as the language adapts to new concepts and social groupings.
Revised:  Our longitudinal analysis reveals that the word niche is far more important than word frequencies in the dynamics of the entire vocabulary at shorter time scales, as the language adapts to new concepts and social groupings.
Edit intent: fluency
Original:  We also identify endogenous versus exogenous value as a further component in the fate of words, and demonstrate the force of this distinction in the rise of novel words.
Revised:  We also distinguish endogenous versus exogenous value as a further component in the fate of words, and demonstrate the force of this distinction in the rise of novel words.
Edit intent: clarity
Original:  We also identify endogenous versus exogenous value as a further component in the fate of words, and demonstrate the force of this distinction in the rise of novel words.
Revised:  We also identify endogenous versus exogenous factors as additional contributors to the fates of words, and demonstrate the force of this distinction in the rise of novel words.
Edit intent: clarity