wanyu/IteraTeR_v2 huggingface dataset:
Original:  We prove that the mixing time of the Swendsen-Wang algorithm for the ferromagnetic Potts model on the n-vertex complete graph satisfies: (i) O(1) for \beta<\beta _{\mathrm{u , (ii) \Theta(n^{1/3}) for \beta=\beta _{\mathrm{u , (iii) \exp(n^{\Omega(1)}) for \beta _{\mathrm{u <\beta<\beta_{ \mathrm{rc }, and (iv) \Theta(\log{n}) for \beta\geq\beta_{ \mathrm{rc }.
Revised:  We prove that the mixing time of the Swendsen-Wang algorithm for the ferromagnetic Potts model on the n-vertex complete graph satisfies: (i) O(1) for \beta<\beta _u , (ii) \Theta(n^{1/3}) for \beta=\beta _{\mathrm{u , (iii) \exp(n^{\Omega(1)}) for \beta _{\mathrm{u <\beta<\beta_{ \mathrm{rc }, and (iv) \Theta(\log{n}) for \beta\geq\beta_{ \mathrm{rc }.
Edit intent: clarity
Original:  We prove that the mixing time of the Swendsen-Wang algorithm for the ferromagnetic Potts model on the n-vertex complete graph satisfies: (i) O(1) for \beta<\beta _{\mathrm{u , (ii) \Theta(n^{1/3}) for \beta=\beta _{\mathrm{u , (iii) \exp(n^{\Omega(1)}) for \beta _{\mathrm{u <\beta<\beta_{ \mathrm{rc }, and (iv) \Theta(\log{n}) for \beta\geq\beta_{ \mathrm{rc }.
Revised:  We prove that the mixing time of the Swendsen-Wang algorithm for the ferromagnetic Potts model on the n-vertex complete graph satisfies: (i) O(1) for \beta<\beta _{\mathrm{u , (ii) \Theta(n^{1/3}) for \beta=\beta _u , (iii) \exp(n^{\Omega(1)}) for \beta _{\mathrm{u <\beta<\beta_{ \mathrm{rc }, and (iv) \Theta(\log{n}) for \beta\geq\beta_{ \mathrm{rc }.
Edit intent: clarity
Original:  We prove that the mixing time of the Swendsen-Wang algorithm for the ferromagnetic Potts model on the n-vertex complete graph satisfies: (i) O(1) for \beta<\beta _{\mathrm{u , (ii) \Theta(n^{1/3}) for \beta=\beta _{\mathrm{u , (iii) \exp(n^{\Omega(1)}) for \beta _{\mathrm{u <\beta<\beta_{ \mathrm{rc }, and (iv) \Theta(\log{n}) for \beta\geq\beta_{ \mathrm{rc }.
Revised:  We prove that the mixing time of the Swendsen-Wang algorithm for the ferromagnetic Potts model on the n-vertex complete graph satisfies: (i) O(1) for \beta<\beta _{\mathrm{u , (ii) \Theta(n^{1/3}) for \beta=\beta _{\mathrm{u , (iii) \exp(n^{\Omega(1)}) for \beta _u <\beta<\beta_{ \mathrm{rc }, and (iv) \Theta(\log{n}) for \beta\geq\beta_{ \mathrm{rc }.
Edit intent: clarity
Original:  We prove that the mixing time of the Swendsen-Wang algorithm for the ferromagnetic Potts model on the n-vertex complete graph satisfies: (i) O(1) for \beta<\beta _{\mathrm{u , (ii) \Theta(n^{1/3}) for \beta=\beta _{\mathrm{u , (iii) \exp(n^{\Omega(1)}) for \beta _{\mathrm{u <\beta<\beta_{ \mathrm{rc }, and (iv) \Theta(\log{n}) for \beta\geq\beta_{ \mathrm{rc }.
Revised:  We prove that the mixing time of the Swendsen-Wang algorithm for the ferromagnetic Potts model on the n-vertex complete graph satisfies: (i) O(1) for \beta<\beta _{\mathrm{u , (ii) \Theta(n^{1/3}) for \beta=\beta _{\mathrm{u , (iii) \exp(n^{\Omega(1)}) for \beta _{\mathrm{u <\beta<\beta_{ rc }, and (iv) \Theta(\log{n}) for \beta\geq\beta_{ \mathrm{rc }.
Edit intent: fluency
Original:  We prove that the mixing time of the Swendsen-Wang algorithm for the ferromagnetic Potts model on the n-vertex complete graph satisfies: (i) O(1) for \beta<\beta _{\mathrm{u , (ii) \Theta(n^{1/3}) for \beta=\beta _{\mathrm{u , (iii) \exp(n^{\Omega(1)}) for \beta _{\mathrm{u <\beta<\beta_{ \mathrm{rc }, and (iv) \Theta(\log{n}) for \beta\geq\beta_{ \mathrm{rc }.
Revised:  We prove that the mixing time of the Swendsen-Wang algorithm for the ferromagnetic Potts model on the n-vertex complete graph satisfies: (i) O(1) for \beta<\beta _{\mathrm{u , (ii) \Theta(n^{1/3}) for \beta=\beta _{\mathrm{u , (iii) \exp(n^{\Omega(1)}) for \beta _{\mathrm{u <\beta<\beta_{ \mathrm{rc }, and (iv) \Theta(\log{n}) for \beta\geq\beta_{ rc }.
Edit intent: fluency
Original:  These results complement refined results of Cuff et al. (2012) on the mixing time of the Glauber dynamics for the ferromagnetic Potts model .
Revised:  These results complement refined results of Cuff et al. on the mixing time of the Glauber dynamics for the ferromagnetic Potts model .
Edit intent: clarity
Original:  In this paper, we con- sider the scenarios of organizing in person friend-making social activities via online social networks (OSNs) and formulate a new research problem, namely, Hop-bounded Maximum Group Friending (HMGF), by modeling both existing friendships and the likelihood of new friend making.
Revised:  In this paper, we consider the scenarios of organizing in person friend-making social activities via online social networks (OSNs) and formulate a new research problem, namely, Hop-bounded Maximum Group Friending (HMGF), by modeling both existing friendships and the likelihood of new friend making.
Edit intent: fluency
Original: The computation of a structured canonical polyadic de-composition (CPD) is useful to address several important modeling problems in real-world applications.
Revised: The computation of a structured canonical polyadic decomposition (CPD) is useful to address several important modeling problems in real-world applications.
Edit intent: clarity
Original:  To estimate them, we formulate specialized estimators based on recently proposed algorithms for the computation of struc-tured CPDs.
Revised:  To estimate them, we formulate specialized estimators based on recently proposed algorithms for the computation of structured CPDs.
Edit intent: fluency
Original:  The first part of this article studies the smoothness and approximability of the solution map, that is, the map a \rightarrow u(a) where a is the parameter value and u(a) is the corresponding solution to the PDE.
Revised:  The first part of this article studies the smoothness and approximability of the solution map, that is, the map a \mapsto u(a) where a is the parameter value and u(a) is the corresponding solution to the PDE.
Edit intent: clarity
Original:  The numerical implemen-tation of these approaches is carried out through adaptive and greedy algorithms.
Revised:  The numerical implementation of these approaches is carried out through adaptive and greedy algorithms.
Edit intent: fluency
Original: When dedicated positioning systems, such as GPS, are unavailable, mobile devices have no choice but to fall back on cellular networks for localization.
Revised: When dedicated positioning systems, such as GPS, are unavailable, a mobile device has no choice but to fall back on cellular networks for localization.
Edit intent: clarity
Original: When dedicated positioning systems, such as GPS, are unavailable, mobile devices have no choice but to fall back on cellular networks for localization.
Revised: When dedicated positioning systems, such as GPS, are unavailable, mobile devices have no choice but to fall back on its cellular network for localization.
Edit intent: clarity
Original:  These, however, are designed primarily with communications goals in mind, where ideally only one base station (BS) is hearable at a given location.
Revised:  Due to random variations in the channel conditions to its surrounding base stations (BS) is hearable at a given location.
Edit intent: clarity
Original:  In this paper, we develop a new tractable approach where we endow the BS locations with a distribution by modeling them as a Poisson Point Process (PPP), and use tools from stochastic geometry to obtain easy-to-use expressions for key performance metrics.
Revised:  In this paper, we develop a new tractable approach where we endow the BS locations with a distribution by modeling them as a Poisson point process (PPP), and use tools from stochastic geometry to obtain easy-to-use expressions for key performance metrics.
Edit intent: fluency
Original:  In particular, we focus on the probability of decoding a given number of BSs at the device of interest , which is shown to be closely coupled with the eventual localization performance .
Revised:  In particular, we focus on the probability of detecting some minimum number of BSs at the device of interest , which is shown to be closely coupled with the eventual localization performance .
Edit intent: clarity
Original:  In particular, we focus on the probability of decoding a given number of BSs at the device of interest , which is shown to be closely coupled with the eventual localization performance .
Revised:  In particular, we focus on the probability of decoding a given number of BSs , which is shown to be closely coupled with the eventual localization performance .
Edit intent: clarity
Original: This paper develops a model that addresses sentence embedding  using recurrent neural networks (RNN) with Long Short Term Memory (LSTM) cells.
Revised: This paper develops a model that addresses sentence embedding using recurrent neural networks (RNN) with Long Short-Term Memory (LSTM) cells.
Edit intent: fluency
Original:  The model automatically attenuates the unimportant words and detects the salient keywords in the sentence.
Revised:  The model is found to automatically attenuate the unimportant words and detects the salient keywords in the sentence.
Edit intent: clarity
Original:  Furthermore, these detected keywords  automatically activate different cells of the LSTM-RNN, where words belonging to a similar topic activate the same cell.
Revised:  Furthermore, these detected keywords are found to automatically activate different cells of the LSTM-RNN, where words belonging to a similar topic activate the same cell.
Edit intent: clarity
Original:  These  keyword detection and topic allocation tasks enabled by the LSTM-RNN allow the network to perform web document retrieval,  where the similarity between the query and documents can be measured by the distance between their corresponding sentence embedding vectors computed by the LSTM-RNN. On a web search task, the LSTM-RNN embedding is shown to significantly outperform all existing state of the art methods.
Revised:  These automatic keyword detection and topic allocation tasks enabled by the LSTM-RNN allow the network to perform web document retrieval, where the similarity between the query and documents can be measured by the distance between their corresponding sentence embedding vectors computed by the LSTM-RNN. On a web search task, the LSTM-RNN embedding is shown to significantly outperform all existing state of the art methods.
Edit intent: clarity
Original:  These  keyword detection and topic allocation tasks enabled by the LSTM-RNN allow the network to perform web document retrieval,  where the similarity between the query and documents can be measured by the distance between their corresponding sentence embedding vectors computed by the LSTM-RNN. On a web search task, the LSTM-RNN embedding is shown to significantly outperform all existing state of the art methods.
Revised:  These keyword detection and topic allocation abilities enabled by the LSTM-RNN allow the network to perform web document retrieval, where the similarity between the query and documents can be measured by the distance between their corresponding sentence embedding vectors computed by the LSTM-RNN. On a web search task, the LSTM-RNN embedding is shown to significantly outperform all existing state of the art methods.
Edit intent: clarity
Original:  These  keyword detection and topic allocation tasks enabled by the LSTM-RNN allow the network to perform web document retrieval,  where the similarity between the query and documents can be measured by the distance between their corresponding sentence embedding vectors computed by the LSTM-RNN. On a web search task, the LSTM-RNN embedding is shown to significantly outperform all existing state of the art methods.
Revised:  These keyword detection and topic allocation tasks enabled by the LSTM-RNN allow the network to perform document retrieval, where the similarity between the query and documents can be measured by the distance between their corresponding sentence embedding vectors computed by the LSTM-RNN. On a web search task, the LSTM-RNN embedding is shown to significantly outperform all existing state of the art methods.
Edit intent: fluency
Original:  These  keyword detection and topic allocation tasks enabled by the LSTM-RNN allow the network to perform web document retrieval,  where the similarity between the query and documents can be measured by the distance between their corresponding sentence embedding vectors computed by the LSTM-RNN. On a web search task, the LSTM-RNN embedding is shown to significantly outperform all existing state of the art methods.
Revised:  These keyword detection and topic allocation tasks enabled by the LSTM-RNN allow the network to perform web document retrieval, where the similarity between the query and documents can be measured by the distance between their corresponding sentence embedding vectors computed by the LSTM-RNN. On a web search task, the LSTM-RNN embedding is shown to significantly outperform several existing state of the art methods.
Edit intent: clarity
Original: This paper develops a model that addresses sentence embedding, a hot topic in current natural language processing research, using recurrent neural networks (RNN) with Long Short-Term Memory (LSTM) cells.
Revised: This paper develops a model that addresses sentence embedding, a hot topic in current natural language processing research, using recurrent neural networks with Long Short-Term Memory (LSTM) cells.
Edit intent: clarity
Original:  The proposed LSTM-RNN model sequentially takes each word in a sentence, extracts its information, and embeds it into a semantic vector.
Edit intent: coherence
Original: The widely-used notion of triadic closure has been conceptualized and measured in a variety of ways, most famously the clustering coefficient.
Revised: Triadic closure has been conceptualized and measured in a variety of ways, most famously the clustering coefficient.
Edit intent: clarity
Original:  In order to avoid arbitrariness, the paper introduces a triadic framework for affiliation networks, within which a range of possible statistics can be considered ;
Revised:  In order to avoid arbitrariness, the paper introduces a triadic framework for affiliation networks, within which a range of measures can be defined ;
Edit intent: clarity
Original: For a class of polynomial kinetic systems, this work examines connections between system parameters, and uniqueness and stability of the resulting equilibria.
Revised: This paper studies the relations among system parameters, and uniqueness and stability of the resulting equilibria.
Edit intent: clarity
Original: For a class of polynomial kinetic systems, this work examines connections between system parameters, and uniqueness and stability of the resulting equilibria.
Revised: For a class of polynomial kinetic systems, this work examines connections between system parameters, uniqueness, and stability of the resulting equilibria.
Edit intent: fluency
Original:  In particular , a canonical representation of the set of all possible feasible equilibrium solutions is developed.
Revised:  In particular , a canonical representation of the set of all possible feasible equilibria is developed.
Edit intent: clarity
Original:  The characterization is made in terms of compartmental matrices which by construction are strictly stable and define the so-called family of solutions.
Revised:  The characterization is made in terms of strictly stable compartmental matrices to define the so-called family of solutions.
Edit intent: clarity
Original:  Feasibility is imposed by a set of constraints, which are linear in the log-transformed space of complexes, and relate to the kernel of the stoichiometric subspace.
Revised:  Feasibility is imposed by a set of constraints, which are linear on a log-transformed space of complexes, and relate to the kernel of the stoichiometric subspace.
Edit intent: clarity
Original:  One particularly interesting representation of these constraints can be established in terms of a class of monotonous functions which turn out to be critical to conclude uniqueness of equilibrium points in a class of deficiency one networks.
Revised:  One particularly interesting representation of these constraints can be expressed in terms of a class of monotonous functions which turn out to be critical to conclude uniqueness of equilibrium points in a class of deficiency one networks.
Edit intent: clarity
Original: Linearizability is the most accepted consistency condition used to describe the semantics of concurrent data structures.
Revised: Linearizability is the most popular consistency condition for concurrent data structures.
Edit intent: clarity
Original:  One of its benefits is its intuitive definition that is well understandable to system designers and programmers.
Revised:  On the one hand, its simplicity makes it accessible to system designers and programmers.
Edit intent: clarity
Original:  However , linearizability is very strong and often linearizable implementations show unsatisfactory performance and scalability.
Revised:  On the other hand , linearizability is very strong and often linearizable implementations show unsatisfactory performance and scalability.
Edit intent: coherence
Original:  However , linearizability is very strong and often linearizable implementations show unsatisfactory performance and scalability.
Revised:  However , linearizability is known to require extensive synchronization resulting in poor performance and scalability.
Edit intent: clarity
Original:  To open up possibilities for more efficient implementations of concurrent data structures, a plethora of consistency conditionshas been considered in the literature .
Revised:  To obtain implementations with better performance, recent research have focused on redefining consistency conditions, i.e. the notion of correctness .
Edit intent: clarity
Original:  Local linearizability is  weaker than linearizability for pools, queues , and stacks.
Revised:  Local linearizability is weaker than linearizability for pools, queues and stacks.
Edit intent: fluency
Original:  In particular, we provide new well-performing and scalable implementations of locally linearizable concurrent queues and stacks .
Revised:  As empirical support to our claims, we present a generic scheme allowing us to obtain locally linearizable implementations out of linearizable ones with much better performance and scalability .
Edit intent: clarity
Original:  On the other hand , linearizability is known to require extensive synchronization resulting in poor performance and scalability.
Revised:  On the other hand , linearizability is known to require extensive synchronization which may jeopardize performance and scalability.
Edit intent: clarity
Original:  Local linearizability is strictly weaker than linearizability on most container types, which include pools, queues  and stacks.
Revised:  Local linearizability is strictly weaker than linearizability on most containers including pools, queues and stacks.
Edit intent: clarity
Original:  Local linearizability is strictly weaker than linearizability on most container types, which include pools, queues  and stacks.
Revised:  Local linearizability is strictly weaker than linearizability on most container types, which include pools, queues , and stacks.
Edit intent: fluency
Original:  For applications that do not require all guarantees offered by linearizability, recent research has therefore focused on improving performance and scalability by relaxing the semantics of concurrent data structures  .
Revised:  For applications that do not require all guarantees offered by linearizability, recent research has focused on improving performance and scalability by relaxing the semantics of concurrent data structures .
Edit intent: coherence
Original:  For applications that do not require all guarantees offered by linearizability, recent research has therefore focused on improving performance and scalability by relaxing the semantics of concurrent data structures  .
Revised:  For applications that do not require all guarantees offered by linearizability, recent research has therefore focused on improving performance and scalability of concurrent data structures .
Edit intent: clarity
Original:  For applications that do not require all guarantees offered by linearizability, recent research has therefore focused on improving performance and scalability by relaxing the semantics of concurrent data structures  .
Revised:  For applications that do not require all guarantees offered by linearizability, recent research has therefore focused on improving performance and scalability by relaxing the semantics of concurrent data structures by relaxing their semantics .
Edit intent: clarity
Original:  In this paper, we present local linearizability, a relaxed consistency condition that is applicable to  pools, queues, stacks, and many other container-type concurrent data structures .
Revised:  In this paper, we present local linearizability, a relaxed consistency condition that is applicable to container-type concurrent data structures like pools, queues, stacks, and many other container-type concurrent data structures .
Edit intent: clarity
Original:  In this paper, we present local linearizability, a relaxed consistency condition that is applicable to  pools, queues, stacks, and many other container-type concurrent data structures .
Revised:  In this paper, we present local linearizability, a relaxed consistency condition that is applicable to pools, queues, and stacks .
Edit intent: clarity
Original:  Local linearizability is strictly weaker than linearizability on most containers including pools, queues, and stacks .
Revised:  We investigate theoretical and practical properties of local linearizability and its relationship to many existing consistency conditions .
Edit intent: clarity
Original:  We present a generic and easy method for implementing locally linearizable data structures using existing linearizable data structures as building blocks.
Revised:  We present a generic implementation method for locally linearizable data structures using existing linearizable data structures as building blocks.
Edit intent: clarity
Original:  We present a generic and easy method for implementing locally linearizable data structures using existing linearizable data structures as building blocks.
Revised:  We present a generic and easy method for implementing locally linearizable data structures that uses existing linearizable data structures as building blocks.
Edit intent: clarity
Original:  In our experiments, our implementations show improvements in performance and scalability compared to the original linearizable building blocks .
Revised:  Our implementations show performance and scalability compared to the original linearizable building blocks .
Edit intent: clarity
Original:  In the past, experiments by Iwasa Tasaki demonstrated small changes in nerve thickness and length during the action potential.
Revised:  Tasaki demonstrated small changes in nerve thickness and length during the action potential.
Edit intent: clarity
Original: Modern memory-optimized clusters entail two levels of networks: connecting CPUs and NUMA regions inside a single server via QPI in the small and multiple servers via Ethernet or Infiniband in the large.
Revised: Modern database clusters entail two levels of networks: connecting CPUs and NUMA regions inside a single server via QPI in the small and multiple servers via Ethernet or Infiniband in the large.
Edit intent: clarity
Original: Modern memory-optimized clusters entail two levels of networks: connecting CPUs and NUMA regions inside a single server via QPI in the small and multiple servers via Ethernet or Infiniband in the large.
Revised: Modern memory-optimized clusters entail two levels of networks: connecting CPUs and NUMA regions inside a single server in the small and multiple servers via Ethernet or Infiniband in the large.
Edit intent: clarity
Original: Modern memory-optimized clusters entail two levels of networks: connecting CPUs and NUMA regions inside a single server via QPI in the small and multiple servers via Ethernet or Infiniband in the large.
Revised: Modern memory-optimized clusters entail two levels of networks: connecting CPUs and NUMA regions inside a single server via QPI in the small and multiple servers in the large.
Edit intent: coherence