wanyu/IteraTeR_v2 huggingface dataset:
Original:  In addition, we show that on a p,q-stochastic block model with two equal sized components, the algorithm recovers the partition in linear time, for p \geq c\cdot N^{-1{2}  } and p/q \geq c{2} + \epsilon} \log N}} .
Revised:  In addition, we show that on a p,q-stochastic block model with p \geq c\cdot N^{-1{2} } and p/q \geq c{2} + \epsilon} \log N}} .
Edit intent: clarity
Original:  In addition, we show that on a p,q-stochastic block model with two equal sized components, the algorithm recovers the partition in linear time, for p \geq c\cdot N^{-1{2}  } and p/q \geq c{2} + \epsilon} \log N}} .
Revised:  In addition, we show that on a p,q-stochastic block model with two equal sized components, the algorithm recovers the partition in linear time, for p \geq c\cdot N^{-1{2} + \epsilon } and p/q \geq c{2} + \epsilon} \log N}} .
Edit intent: fluency
Original:  In this paper we consider the number of tweets (tweet volume) of a party as a proxy of collective attention to the party, we identify the dynamics of the volume, and show that this quantity has some information on the elections outcome.
Revised:  In this paper we consider the number of tweets (tweet volume) of a party as a proxy of collective attention to the party, identify the dynamics of the volume, and show that this quantity has some information on the elections outcome.
Edit intent: fluency
Original:  We find that the distribution of the tweet volume for each party follows a log-normal distribution with a positive autocorrelation  over short terms  .
Revised:  We find that the distribution of the tweet volume for each party follows a log-normal distribution with a positive autocorrelation of the volume over short terms .
Edit intent: clarity
Original:  We define the Shannon gate complexity function L(n,q) and the depth function D(n,q) as functions of n and a number of additional inputs q. First, we prove general lower asymptotic bounds for functions L(n,q) and D(n,q).
Revised:  We define the Shannon gate complexity function L(n,q) and the depth function D(n,q) as functions of n and the number of additional inputs q. First, we prove general lower asymptotic bounds for functions L(n,q) and D(n,q).
Edit intent: fluency
Original:  We define the Shannon gate complexity function L(n,q) and the depth function D(n,q) as functions of n and a number of additional inputs q. First, we prove general lower asymptotic bounds for functions L(n,q) and D(n,q).
Revised:  We define the Shannon gate complexity function L(n,q) and the depth function D(n,q) as functions of n and a number of additional inputs q. First, we prove general lower bounds for functions L(n,q) and D(n,q).
Edit intent: clarity
Original:  %DIFDELCMD < \lesssim %%% 52n 2 ^n \mathop / \log_2 n. Using those asymptotic bounds, we state that almost every reversible circuit with no additional inputs, consisting of NOT, CNOT and 2-CNOT gates, implements a transformation from F(n,0) with the gate complexity L(n,0) \asymp n 2^n \mathop / \log_2 n and  the depth D(n,0) %DIFDELCMD < \gtrsim %%%  2 ^{n-1 \mathop /  \log_2 n  .
Revised:  %DIFDELCMD < \lesssim %%% 52n 2 ^n \mathop / \log_2 n. Using these bounds, we state that almost every reversible circuit with no additional inputs, consisting of NOT, CNOT and 2-CNOT gates, implements a transformation from F(n,0) with the gate complexity L(n,0) \asymp n 2^n \mathop / \log_2 n and the depth D(n,0) %DIFDELCMD < \gtrsim %%% 2 ^{n-1 \mathop / \log_2 n .
Edit intent: clarity
Original:  %DIFDELCMD < \lesssim %%% 52n 2 ^n \mathop / \log_2 n. Using those asymptotic bounds, we state that almost every reversible circuit with no additional inputs, consisting of NOT, CNOT and 2-CNOT gates, implements a transformation from F(n,0) with the gate complexity L(n,0) \asymp n 2^n \mathop / \log_2 n and  the depth D(n,0) %DIFDELCMD < \gtrsim %%%  2 ^{n-1 \mathop /  \log_2 n  .
Revised:  %DIFDELCMD < \lesssim %%% 52n 2 ^n \mathop / \log_2 n. Using those asymptotic bounds, we state that almost every reversible circuit with no additional inputs, consisting of NOT, CNOT and 2-CNOT gates, implements a transformation from F(n,0) with the gate complexity L(n,0) \asymp n 2^n \mathop / \log_2 n and with the depth D(n,0) %DIFDELCMD < \gtrsim %%% 2 ^{n-1 \mathop / \log_2 n .
Edit intent: fluency
Original:  %DIFDELCMD < \lesssim %%% 52n 2 ^n \mathop / \log_2 n. Using those asymptotic bounds, we state that almost every reversible circuit with no additional inputs, consisting of NOT, CNOT and 2-CNOT gates, implements a transformation from F(n,0) with the gate complexity L(n,0) \asymp n 2^n \mathop / \log_2 n and  the depth D(n,0) %DIFDELCMD < \gtrsim %%%  2 ^{n-1 \mathop /  \log_2 n  .
Revised:  %DIFDELCMD < \lesssim %%% 52n 2 ^n \mathop / \log_2 n. Using those asymptotic bounds, we state that almost every reversible circuit with no additional inputs, consisting of NOT, CNOT and 2-CNOT gates, implements a transformation from F(n,0) with the gate complexity L(n,0) \asymp n 2^n \mathop / \log_2 n and the depth D(n,0) %DIFDELCMD < \gtrsim %%% \geq 2 ^{n-1 \mathop / \log_2 n .
Edit intent: clarity
Original:  %DIFDELCMD < \lesssim %%% 52n 2 ^n \mathop / \log_2 n. Using those asymptotic bounds, we state that almost every reversible circuit with no additional inputs, consisting of NOT, CNOT and 2-CNOT gates, implements a transformation from F(n,0) with the gate complexity L(n,0) \asymp n 2^n \mathop / \log_2 n and  the depth D(n,0) %DIFDELCMD < \gtrsim %%%  2 ^{n-1 \mathop /  \log_2 n  .
Revised:  %DIFDELCMD < \lesssim %%% 52n 2 ^n \mathop / \log_2 n. Using those asymptotic bounds, we state that almost every reversible circuit with no additional inputs, consisting of NOT, CNOT and 2-CNOT gates, implements a transformation from F(n,0) with the gate complexity L(n,0) \asymp n 2^n \mathop / \log_2 n and the depth D(n,0) %DIFDELCMD < \gtrsim %%% 2 ^{n-1 \mathop / \log_2 n ) .
Edit intent: fluency
Original:  Second, we introduce a new group theory based synthesis algorithm, which can produce a circuit \mathfrak S without additional inputs and with  gate complexity L(\mathfrak S)
Revised:  Second, we introduce a new group theory based synthesis algorithm, which can produce a circuit \mathfrak S without additional inputs and with the gate complexity L(\mathfrak S)
Edit intent: fluency
Original:  Here, we overcome this theoretical obstacle , and we present a formal definition of common neighbour index (CN) and local-community-paradigm (LCP) for bipartite networks.
Revised:  Here, we overcome this theoretical obstacle and present a formal definition of common neighbour index (CN) and local-community-paradigm (LCP) for bipartite networks.
Edit intent: fluency
Original:  As a consequence, we are able to introduce the first node-neighbourhood-based and LCP-based models for topological link prediction that utilizes the bipartite domain.
Revised:  As a consequence, we are able to introduce the first node-neighbourhood-based and LCP-based models for topological link prediction that utilize the bipartite domain.
Edit intent: fluency
Original:  To apply it to our case, we introduce a new construction called a ``lifted language''.
Revised:  To apply it to our case, we introduce a new construction called a "lifted language."
Edit intent: fluency
Original:  This paper proposes hypervisor-enforced timing mitigation to control timing channels in cloud environments.
Revised:  We propose hypervisor-enforced timing mitigation to control timing channels in cloud environments.
Edit intent: clarity
Original:  Our prototype hypervisor implementation is the first system that can mitigate timing-channel leakage across full-scale existing operating systems such as Linux and applications written in arbitrary languages.
Revised:  Our prototype hypervisor is the first system that can mitigate timing-channel leakage across full-scale existing operating systems such as Linux and applications written in arbitrary languages.
Edit intent: clarity
Original:  Our prototype hypervisor implementation is the first system that can mitigate timing-channel leakage across full-scale existing operating systems such as Linux and applications written in arbitrary languages.
Revised:  Our prototype hypervisor implementation is the first system to mitigate timing-channel leakage across full-scale existing operating systems such as Linux and applications written in arbitrary languages.
Edit intent: clarity
Original:  Our prototype hypervisor implementation is the first system that can mitigate timing-channel leakage across full-scale existing operating systems such as Linux and applications written in arbitrary languages.
Revised:  Our prototype hypervisor implementation is the first system that can mitigate timing-channel leakage across full-scale existing operating systems such as Linux and applications in arbitrary languages.
Edit intent: clarity
Original: Populations of mammalian progenitor cells commonly exhibit considerable cell-cell variability.
Revised: Populations of mammalian stem cells commonly exhibit considerable cell-cell variability.
Edit intent: clarity
Original:  Here, we analyze the dynamics of the stem cell surface marker Sca1 in mouse hematopoietic progenitor cells using a simple stochastic model and propose that multipotency is an example of maximum entropy statistical inference : in the absence of defined instructions, individual cells remain maximally non-committal with respect to their molecular identity, thereby generating a maximally diverse population that is able to respond optimally to a wide range of unforeseen future environmental changes.
Revised:  Here, we analyze expression fluctuations of the stem cell surface marker Sca1 in mouse hematopoietic progenitor cells using a simple stochastic model and propose that multipotency is an example of maximum entropy statistical inference : in the absence of defined instructions, individual cells remain maximally non-committal with respect to their molecular identity, thereby generating a maximally diverse population that is able to respond optimally to a wide range of unforeseen future environmental changes.
Edit intent: clarity
Original:  Here, we analyze expression fluctuations of the stem cell surface marker Sca1 in mouse hematopoietic progenitor cells using a simple stochastic model and find that  observed dynamics naturally self-organize close to a critical state with near-optimal information-processing capacity .
Revised:  Here, we analyze expression fluctuations of the stem cell surface marker Sca1 in mouse hematopoietic progenitor cells using a simple stochastic model and find that the observed dynamics naturally self-organize close to a critical state with near-optimal information-processing capacity .
Edit intent: fluency
Original:  Here, we analyze expression fluctuations of the stem cell surface marker Sca1 in mouse hematopoietic progenitor cells using a simple stochastic model and find that  observed dynamics naturally self-organize close to a critical state with near-optimal information-processing capacity .
Revised:  Here, we analyze expression fluctuations of the stem cell surface marker Sca1 in mouse hematopoietic progenitor cells using a simple stochastic model and find that observed dynamics naturally lie close to a critical state with near-optimal information-processing capacity .
Edit intent: clarity
Original:  somewhat more than one million papers when primary research articles are considered only . Sophisticated and compact bibliometric methods have to be applied in order to obtain an overview.
Revised:  somewhat more than one million papers when primary research papers are considered only . Sophisticated and compact bibliometric methods have to be applied in order to obtain an overview.
Edit intent: fluency
Original:  somewhat more than one million papers when primary research articles are considered only . Sophisticated and compact bibliometric methods have to be applied in order to obtain an overview.
Revised:  somewhat more than one million papers when primary research articles are considered only (articles and reviews are the document types where primary research is usually reported or reviewed). However, who reads these papers? More precisely, which groups of researchers from which (self-assigned) scientific disciplines and countries are reading these papers? Are there readership patterns visible for certain countries, scientific disciplines, or academic status groups?
Edit intent: coherence
Original:  One popular method is a network-based analysis.
Revised:  One popular method to answer these questions is a network analysis.
Edit intent: clarity
Original:  Are there readership patterns visible for certain countries, scientific disciplines, or academic status groups?
Revised:  Is it possible to visualize readership patterns for certain countries, scientific disciplines, or academic status groups?
Edit intent: clarity
Original:  (3) The country network focusses on global readership patterns: a group of 53 nations is identified as core to the scientific enterprise, including most OECD countries, Russia , and China .
Revised:  (3) The country network focusses on global readership patterns: a group of 53 nations is identified as core to the scientific enterprise, including Russia and China as well as two thirds of the OECD (Organisation for Economic Co-operation and Development) countries .
Edit intent: clarity
Original:  We find a simple analytical formula for the power spectrum of the neural field in the case of a istantaneous and localized external stimulus .
Revised:  We find a simple analytical formula for the power spectrum of the neural field . In the case of a istantaneous and localized external stimulus .
Edit intent: fluency
Original:  We find a simple analytical formula for the power spectrum of the neural field in the case of a istantaneous and localized external stimulus .
Revised:  We find a simple analytical formula for the power spectrum of the neural field in the case of an istantaneous and localized external stimulus .
Edit intent: fluency
Original:  In the regime of small wavenumber and large frequency we show that  the power spectrum scales as 1/\omega^2, in good agreement with several data of electroencephalography and functional magnetic resonance imaging of brain neocortex.
Revised:  In the regime of small wavenumber and large frequency we show that the power spectrum scales as 1/\omega^2, in agreement with experimental data of electroencephalography and functional magnetic resonance imaging of brain neocortex.
Edit intent: clarity
Original:  For some initial conditions, we discuss exact and approximate analytical solutions of this reaction-diffusion equation.
Revised:  For some initial conditions, we discuss analytical solutions of this reaction-diffusion equation.
Edit intent: clarity
Original:  In the case of an istantaneous and localized external stimulus, we show that for large frequencies \omega the power spectrum scales as 1/\omega^2 , in agreement with experimental data of electroencephalography .
Revised:  In the case of an istantaneous and localized external stimulus, we show that for large frequencies \omega the power spectrum scales as 1/\omega^2 .
Edit intent: coherence
Original:  By considering a small perturbation with respect to a stationary and uniform configuration of the neural field we derive a linearized equation which is solved for a generic external stimulus by using the Fourier transform into wavevector-freqency domain, finding an elegant analytical formula for the power spectrum of the neural field.
Revised:  By considering a small perturbation with respect to a stationary and uniform configuration of the neural field we derive a linearized equation which is solved for a generic external stimulus by using the Fourier transform into wavevector-freqency domain, finding an analytical formula for the power spectrum of the neural field.
Edit intent: clarity
Original: Resource constrained shortest path problems are usually solved by label algorithms, which consist in a smart enumeration of  the non-dominated paths.
Revised: Resource constrained shortest path problems are usually solved thanks to a smart enumeration of the non-dominated paths.
Edit intent: clarity
Original: Resource constrained shortest path problems are usually solved by label algorithms, which consist in a smart enumeration of  the non-dominated paths.
Revised: Resource constrained shortest path problems are usually solved by label algorithms, which consist in a smart enumeration of all the non-dominated paths.
Edit intent: clarity
Original:  Recent improvements of these  algorithms rely on the use of bounds on path resources to discard partial solutions.
Revised:  Recent improvements of these enumeration algorithms rely on the use of bounds on path resources to discard partial solutions.
Edit intent: clarity
Original:  We use lattice theory to provide a polynomial procedure to find good quality bounds.
Revised:  We use lattice theory to provide polynomial procedures to find good quality bounds.
Edit intent: fluency
Original:  We apply our data mining algorithm and interestingness measures to gene expression datasets from the Gene Expression Database at the Mouse Genomics Institute as a preliminary proof of concept to mine relationships between developmental stages in the mouse anatomy ontology and Gene Ontology concepts (biological process, molecular function and cellular component).
Revised:  We apply our data mining algorithm and interestingness measures to datasets from the Gene Expression Database at the Mouse Genomics Institute as a preliminary proof of concept to mine relationships between developmental stages in the mouse anatomy ontology and Gene Ontology concepts (biological process, molecular function and cellular component).
Edit intent: fluency
Original:  \mbox{ cranston\dots graphs are antimagic for k%DIFDELCMD < \ge %%% 2.
Revised:  \mbox{ cranston\dots graphs are antimagic %DIFDELCMD < \ge %%% 2.
Edit intent: clarity
Original: In this work, we propose a fast, robust and scalable method for retrieving and analyzing recurring patterns of activity induced by a causal process, typically modeled as time series on a graph.
Revised: In this work, we propose a fast, robust and scalable framework for retrieving and analyzing recurring patterns of activity induced by a causal process, typically modeled as time series on a graph.
Edit intent: clarity
Original:  Recently, new research topics devoted to the analysis of graphs and data associated to their vertices have emerged.
Revised:  Recently, new research areas devoted to the analysis of graphs and data associated to their vertices have emerged.
Edit intent: clarity
Original:  First , we study how rumor spreads on  social network.
Revised:  Firstly , we study how rumor spreads on social network.
Edit intent: fluency
Original:  First , we study how rumor spreads on  social network.
Revised:  First , we study how rumor spreads on a social network.
Edit intent: fluency
Original:  Second , we reveal congestion patterns of pedestrians in a train station.
Revised:  Secondly , we reveal congestion patterns of pedestrians in a train station.
Edit intent: coherence
Original:  In each example, relevant information previously hidden in the data is extracted in a very efficient manner emphasizing on the scalability of our method : with a parallel implementation scaling linearly with the size of the dataset, our framework easily handles millions of nodes on a single commodity server.
Revised:  In each example, relevant information previously hidden in the data is extracted in a very efficient manner , emphasizing the scalability of our method : with a parallel implementation scaling linearly with the size of the dataset, our framework easily handles millions of nodes on a single commodity server.
Edit intent: fluency
Original:  In each example, relevant information previously hidden in the data is extracted in a very efficient manner emphasizing on the scalability of our method : with a parallel implementation scaling linearly with the size of the dataset, our framework easily handles millions of nodes on a single commodity server.
Revised:  In each example, relevant information previously hidden in the data is extracted in a very efficient manner emphasizing on the scalability of our method . With a parallel implementation scaling linearly with the size of the dataset, our framework easily handles millions of nodes on a single commodity server.
Edit intent: fluency
Original: We consider a setting where multiple users share multiple channels modeled as a multi-user multi-armed bandit (MAB) problem.
Revised: We consider a setting where multiple users share several channels modeled as a multi-user multi-armed bandit (MAB) problem.
Edit intent: fluency
Original:  The characteristics of each channel are initially unknown and may differ between the users . Each user can choose between the channels, but her success depends on the particular channel  as well as on the selections of other users: if two users select the same channel their messages collide and none of them manages to send any data.
Revised:  The characteristics of each channel are unknown and are different for each user . Each user can choose between the channels, but her success depends on the particular channel as well as on the selections of other users: if two users select the same channel their messages collide and none of them manages to send any data.
Edit intent: clarity
Original:  The characteristics of each channel are initially unknown and may differ between the users . Each user can choose between the channels, but her success depends on the particular channel  as well as on the selections of other users: if two users select the same channel their messages collide and none of them manages to send any data.
Revised:  The characteristics of each channel are initially unknown and may differ between the users . Each user can choose between the channels, but her success depends on the particular channel chosen as well as on the selections of other users: if two users select the same channel their messages collide and none of them manages to send any data.
Edit intent: clarity
Original:  Our setting is fully distributed, so there is no central control and every user only observes the channel she currently uses .
Revised:  Our setting is fully distributed, so there is no central control .
Edit intent: clarity
Original:  As in many communication systems such as cognitive radio networks , the users cannot communicate among themselves so coordination must be achieved without direct communication .
Revised:  As in many communication systems , the users cannot communicate among themselves so coordination must be achieved without direct communication .
Edit intent: clarity
Original:  As in many communication systems such as cognitive radio networks , the users cannot communicate among themselves so coordination must be achieved without direct communication .
Revised:  As in many communication systems such as cognitive radio networks , the users cannot set up a direct communication protocol, so information exchange must be limited to a minimum .
Edit intent: clarity
Original:  We develop algorithms for learning a stable configuration for the multiple user MAB problem.
Revised:  We develop an algorithm for learning a stable configuration for the multiple user MAB problem.
Edit intent: fluency
Original:  We develop algorithms for learning a stable configuration for the multiple user MAB problem.
Revised:  We develop algorithms for learning a stable configuration for the multi-user MAB problem.
Edit intent: fluency
Original:  The remaining parameter space of the model, which corresponds to diverging MT lengths, is analyzed by means of extensive Monte-Carlo simulations and a macroscopic approach.
Revised:  The remaining parameter space of the model, which corresponds to diverging MT lengths, is analyzed by means of extensive Monte Carlo simulations and a macroscopic approach.
Edit intent: fluency