wanyu/IteraTeR_v2 huggingface dataset:
Original:  This fact inspires us to propose a new, practical working hypothesis, called the linear space hypothesis (LSH), which states that 2SAT_3 --a restricted variant of 2SAT in which each variable of a given 2CNF formula appears as literals in at most 3 clauses--cannot be solved simultaneously in polynomial time using strictly "sub-linear" (i.e., n^e polylog(n\, polylog(|x|} ) for a certain constant e in (0,1) ) space .
Revised:  This fact inspires us to propose a new, practical working hypothesis, called the linear space hypothesis (LSH), which states that 2SAT_3 --a restricted variant of 2SAT in which each variable of a given 2CNF formula appears as literals in at most 3 times in the form of literals---cannot be solved simultaneously in polynomial time using strictly "sub-linear" (i.e., n^e polylog(n\, polylog(|x|} ) for a certain constant e in (0,1) ) space .
Edit intent: clarity
Original:  In particular, we prove that, if for given n, k such family exists, then n%DIFDELCMD < \le %%% k^2-k+1.
Revised:  In particular, we %DIFDELCMD < \le %%% k^2-k+1.
Edit intent: coherence
Original: We used to marry people to which we were somehow connected to: friends of friends, schoolmates, neighbours . Since we were more connected to people similar to us, we were  likely to marry someone from our own race.
Revised: We used to marry people to whom we were somehow connected to: friends of friends, schoolmates, neighbours . Since we were more connected to people similar to us, we were likely to marry someone from our own race.
Edit intent: fluency
Original: We used to marry people to which we were somehow connected to: friends of friends, schoolmates, neighbours . Since we were more connected to people similar to us, we were  likely to marry someone from our own race.
Revised: We used to marry people to which we were somehow connected . Since we were more connected to people similar to us, we were likely to marry someone from our own race.
Edit intent: coherence
Original: We used to marry people to which we were somehow connected to: friends of friends, schoolmates, neighbours . Since we were more connected to people similar to us, we were  likely to marry someone from our own race.
Revised: We used to marry people to which we were somehow connected to: friends of friends, schoolmates, neighbours . Since we were more connected to people similar to us, we were also likely to marry someone from our own race.
Edit intent: coherence
Original:  However, online dating has changed this pattern : people who meet online tend to be complete strangers.
Revised:  However, online dating has changed this pattern ; people who meet online tend to be complete strangers.
Edit intent: fluency
Original:  Given that one-third of modern marriages start online, we investigate theoretically, using random graphs and matching theory, the effects of those previously absent ties in the diversity of modern societies.
Revised:  We investigate the effects of those previously absent ties in the diversity of modern societies.
Edit intent: coherence
Original:  Given that one-third of modern marriages start online, we investigate theoretically, using random graphs and matching theory, the effects of those previously absent ties in the diversity of modern societies.
Revised:  Given that one-third of modern marriages start online, we investigate theoretically, using random graphs and matching theory, the effects of those previously absent ties on the diversity of modern societies.
Edit intent: clarity
Original:  Increasing computational efficiency allowed us to produce VBA results in 1-3 days for large multidimensional arrays which previously took 1 month.
Revised:  The increased computational efficiency allowed us to produce VBA results in 1-3 days for large multidimensional arrays which previously took 1 month.
Edit intent: clarity
Original:  Increasing computational efficiency allowed us to produce VBA results in 1-3 days for large multidimensional arrays which previously took 1 month.
Revised:  Increasing computational efficiency allowed large multidimensional arrays to be processed in 1-3 days for large multidimensional arrays which previously took 1 month.
Edit intent: clarity
Original:  Increasing computational efficiency allowed us to produce VBA results in 1-3 days for large multidimensional arrays which previously took 1 month.
Revised:  Increasing computational efficiency allowed us to produce VBA results in 1-3 days , a task that previously took ~ 1 month.
Edit intent: clarity
Original:  To address the need for quantitative VBA validation we propose a  framework consisting of morphological phantoms, and four quantitative metrics.
Revised:  To quantify the variability and reliability of preclinical VBA in rodent models, we propose a framework consisting of morphological phantoms, and four quantitative metrics.
Edit intent: clarity
Original:  To address the need for quantitative VBA validation we propose a  framework consisting of morphological phantoms, and four quantitative metrics.
Revised:  To address the need for quantitative VBA validation we propose a validation framework consisting of morphological phantoms, and four quantitative metrics.
Edit intent: fluency
Original:  We address several factors that impact VBA results, including registration parameters, and template construction strategies.
Revised:  We address several factors that impact VBA results, including registration and template construction strategies.
Edit intent: clarity
Original:  Due to shorter processing times, we could explore multiple parameter sets, and VBA stability.
Edit intent: coherence
Original:  We have used this framework to guide the selection of spatial registration parameters in a VBA study for a mouse model of epilepsy.
Revised:  We have used this framework to inform the VBA workflow parameters in a VBA study for a mouse model of epilepsy.
Edit intent: clarity
Original:  By these innovations, the network performance in CBRT is much better than that in ExOR ;
Revised:  By these innovations, the network performance in CBRT is much better than that in ExOR ,
Edit intent: fluency
Original: The increased network flexibility introduced by new technologies, such as Software-Defined Networking, are motivating operators to consider running their networks at higher utilization levels.
Revised: The increased network flexibility introduced by new technologies, such as Software-Defined Networking, let operators consider running their networks at higher utilization levels.
Edit intent: clarity
Original:  Traditionally, networks were operated at a small fraction of the network capacity (30-40\%);
Revised:  Traditionally, networks were operated at a small fraction of their capacities (30-40\%);
Edit intent: clarity
Original:  recently, however, operators are considering running the network harder (60\% utilization and above 1 ).
Revised:  recently, however, operators are considering running their networks harder (60\% utilization and above 1 ).
Edit intent: fluency
Original:  recently, however, operators are considering running the network harder (60\% utilization and above 1 ).
Revised:  recently, however, operators are considering running the network harder (60\% utilization and above ).
Edit intent: fluency
Original:  Higher utilization can increase the network operator's revenue, but this gain comes at a cost: daily traffic fluctuations and failures might result in the networknot being able to carry all offered traffic .
Revised:  Higher utilization can increase the network operator's revenue, but this gain comes at a cost: daily traffic fluctuations and failures might overload the network .
Edit intent: clarity
Original:  We focus on the scenario of demands with flexible bandwidth requirements, e.g., allocated connections might undergo service degradations to allow for a new connection to be provisioned - a demand that would otherwise be blocked.
Revised:  We focus on settings with flexible bandwidth requirements, e.g., allocated connections might undergo service degradations to allow for a new connection to be provisioned - a demand that would otherwise be blocked.
Edit intent: clarity
Original:  We focus on the scenario of demands with flexible bandwidth requirements, e.g., allocated connections might undergo service degradations to allow for a new connection to be provisioned - a demand that would otherwise be blocked.
Revised:  We focus on the scenario of demands with flexible bandwidth requirements, e.g., allocated connections can tolerate service degradation. This can allow a new connection to be provisioned - a demand that would otherwise be blocked.
Edit intent: clarity
Original:  We focus on the scenario of demands with flexible bandwidth requirements, e.g., allocated connections might undergo service degradations to allow for a new connection to be provisioned - a demand that would otherwise be blocked.
Revised:  We focus on the scenario of demands with flexible bandwidth requirements, e.g., allocated connections might undergo service degradations to allow for a new connection to be provisioned - a connection that would otherwise be blocked.
Edit intent: clarity
Original:  In these situations, it is important that the network operator makes an informed decision, since degrading a high-paying connection to allocate a low-value demand is not sensible.
Revised:  In these situations, the network operator makes an informed decision, since degrading a high-paying connection to allocate a low-value demand is not sensible.
Edit intent: clarity
Original:  In these situations, it is important that the network operator makes an informed decision, since degrading a high-paying connection to allocate a low-value demand is not sensible.
Revised:  In these situations, it is important that the network operator needs to make an informed decision, since degrading a high-paying connection to allocate a low-value demand is not sensible.
Edit intent: clarity
Original:  In these situations, it is important that the network operator makes an informed decision, since degrading a high-paying connection to allocate a low-value demand is not sensible.
Revised:  In these situations, it is important that the network operator makes an informed decision, since degrading a high-paying connection to allocate a low-value connection is not sensible.
Edit intent: clarity
Original:  Accordingly, we show that, during Resource Crunch, the decision of whether or not to serve a demand (and which other connections to degrade) focusing on maximizing profits is of complex nature.
Revised:  We offer strategies for deciding whether or not to serve a demand (and which other connections to degrade) focusing on maximizing profits is of complex nature.
Edit intent: clarity
Original:  Accordingly, we show that, during Resource Crunch, the decision of whether or not to serve a demand (and which other connections to degrade) focusing on maximizing profits is of complex nature.
Revised:  Accordingly, we show that, during Resource Crunch, the decision of whether or not to serve a connection (and which other connections to degrade) focusing on maximizing profits is of complex nature.
Edit intent: clarity
Original:  In this study, we propose an abstraction of the network state, called  Connection Adjacency Graph (CAG), to devise an efficient method to decide whether or not to serve a demand, and which other connections to degrade.
Revised:  In this study, we propose an abstraction of the network state, called a Connection Adjacency Graph (CAG), to devise an efficient method to decide whether or not to serve a demand, and which other connections to degrade.
Edit intent: fluency
Original:  In this study, we propose an abstraction of the network state, called  Connection Adjacency Graph (CAG), to devise an efficient method to decide whether or not to serve a demand, and which other connections to degrade.
Revised:  In this study, we propose an abstraction of the network state, called Connection Adjacency Graph (CAG), to devise an efficient methods to decide whether or not to serve a demand, and which other connections to degrade.
Edit intent: fluency
Original:  We compare our method to existing greedy approaches and show that we outperform them during Resource Crunch.
Revised:  We compare our method to existing greedy approaches and show that our method outperforms them during Resource Crunch.
Edit intent: fluency
Original: The increased network flexibility introduced by new technologies, such as Software-Defined Networking, let operators consider running their networks at higher utilization levels.
Edit intent: coherence
Original:  Traditionally, networks were operated at a small fraction of their capacities (30-40\%);
Revised:  Traditionally, networks operate at a small fraction of their capacities (30-40\%);
Edit intent: fluency
Original:  Higher utilization can increase the network operator's revenue, but this gain comes at a cost: daily traffic fluctuations and failures might  overload the network.
Revised:  Higher utilization can increase the network operator's revenue, but this gain comes at a cost: daily traffic fluctuations and failures might occasionally overload the network.
Edit intent: clarity
Original:  We call such network congestion situations Resource Crunch.
Revised:  We call such situations Resource Crunch.
Edit intent: clarity
Original:  We focus on settings with flexible bandwidth requirements, e.g., allocated connections can tolerate service degradation.
Revised:  We focus on scenarios with flexible bandwidth requirements, e.g., allocated connections can tolerate service degradation.
Edit intent: clarity
Original:  We focus on settings with flexible bandwidth requirements, e.g., allocated connections can tolerate service degradation.
Revised:  We focus on settings with flexible bandwidth requirements, e.g., some connections can tolerate service degradation.
Edit intent: clarity
Original:  In these situations , the network operator needs to make an informed decision, since degrading a high-paying connection to allocate a low-value connection is not sensible.
Revised:  For that , the network operator needs to make an informed decision, since degrading a high-paying connection to allocate a low-value connection is not sensible.
Edit intent: clarity
Original:  In these situations , the network operator needs to make an informed decision, since degrading a high-paying connection to allocate a low-value connection is not sensible.
Revised:  In these situations , the network operator needs to make an informed decision, since reducing the bandwidth of a high-paying connection to allocate a low-value connection is not sensible.
Edit intent: clarity
Original:  We offer strategies for deciding whether or not to serve a connection (and which other connections to degrade) focusing on maximizing profits during Resource Crunch.
Revised:  We propose a strategy to decide whether or not to serve a connection (and which other connections to degrade) focusing on maximizing profits during Resource Crunch.
Edit intent: clarity
Original:  We offer strategies for deciding whether or not to serve a connection (and which other connections to degrade) focusing on maximizing profits during Resource Crunch.
Revised:  We offer strategies for deciding whether or not to provision a request (and which other connections to degrade) focusing on maximizing profits during Resource Crunch.
Edit intent: clarity
Original:  Our solutions use a new abstraction of the network state, called a Connection Adjacency Graph (CAG) , to devise an efficient methods to decide whether or not to serve a demand, and which other connections to degrade.
Revised:  To address this problem, we use an abstraction of the network state, called a Connection Adjacency Graph (CAG) , to devise an efficient methods to decide whether or not to serve a demand, and which other connections to degrade.
Edit intent: clarity
Original:  In this paper, we propose a novel HUman and Machine cOoperative (HUMO) framework for entity resolution (ER), which divides an ER workload between machine and human.
Revised:  In this paper, we propose a novel HUman and Machine cOoperation (HUMO) framework for entity resolution (ER), which divides an ER workload between machine and human.
Edit intent: fluency
Original:  In this paper, we propose a novel HUman and Machine cOoperative (HUMO) framework for entity resolution (ER), which divides an ER workload between machine and human.
Revised:  In this paper, we propose a novel HUman and Machine cOoperative (HUMO) framework for entity resolution (ER), which divides an ER workload between the machine and the human.
Edit intent: fluency
Original:  Finally, we demonstrate by extensive experiments on real and synthetic datasets that HUMO can achieve high-quality results with reasonable return on investment (ROI) in terms of human cost, and it performs considerably better than the state-of-the-art alternative in quality control.
Revised:  Finally, we demonstrate by extensive experiments on real and synthetic datasets that HUMO can achieve high-quality results with reasonable return on investment (ROI) in terms of human cost, and it performs considerably better than the state-of-the-art alternatives in quality control.
Edit intent: fluency
Original: This paper aims to investigate the strong convergence analysis of the exponential Euler method for parabolic stochastic partial differential equation (SPDE) driven by additive noise under more relaxed conditions .
Revised: This paper deals with the numerical approximation of semilinear parabolic stochastic partial differential equation (SPDE) driven by additive noise under more relaxed conditions .
Edit intent: clarity
Original:  The SPDE is discretized in space by the finite element method .
Revised:  The SPDE is discretized in space with the standard finite element method .
Edit intent: clarity
Original: In  particular, for trace class  noise we achieve convergence orders of O(h ^{2 +\Delta t )).
Revised: In particular, for trace class noise we achieve convergence order O(h ^{2 +\Delta t )).
Edit intent: clarity
Original: In  particular, for trace class  noise we achieve convergence orders of O(h ^{2 +\Delta t )).
Revised: In particular, for trace class noise we achieve convergence orders of O(h ^2 +\Delta t )).
Edit intent: fluency
Original: For additive trace class Gaussian noise and an appropriate jump function, we achieve convergence order O(h^2+\Delta t)} . These optimal convergence orders are due to a new optimal regularity result we have further derived here, which was not yet proved in the literature, even in the case of self-adjoint operator.
Revised: For additive trace class Gaussian noise and an appropriate jump function, we achieve convergence order O(h^2+\Delta t)} . 
Edit intent: coherence
Original:  Numerical experiments to illustrate our theoretical result are provided.
Revised:  Numerical experiments to sustain the theoretical results are provided.
Edit intent: clarity
Original: A resistive deep belief network ( R-DBN ) architecture is developed using the physics of nanomagnets to provide a natural hardware representation for individual probabilistic neurons.
Revised: A low-energy hardware implementation of deep belief network ( R-DBN ) architecture is developed using the physics of nanomagnets to provide a natural hardware representation for individual probabilistic neurons.
Edit intent: clarity
Original: A resistive deep belief network ( R-DBN ) architecture is developed using the physics of nanomagnets to provide a natural hardware representation for individual probabilistic neurons.
Revised: A resistive deep belief network ( DBN ) architecture is developed using the physics of nanomagnets to provide a natural hardware representation for individual probabilistic neurons.
Edit intent: clarity
Original:  Probabilistic spin logic devices (p-bits)  are modeled to demonstrate a sigmoidal activation function.
Revised:  Probabilistic spin logic devices (p-bits) , which are modeled to demonstrate a sigmoidal activation function.
Edit intent: coherence
Original:  A hybrid CMOS/spin based weighted array structure is designed to implement a restricted Boltzmann machine (RBM). Device-level simulations based on precise physics relations are used to validate the sigmoidal relation between the output probability of a p-bit and its input currents.
Revised:  A CMOS/spin based weighted array structure is designed to implement a restricted Boltzmann machine (RBM). Device-level simulations based on precise physics relations are used to validate the sigmoidal relation between the output probability of a p-bit and its input currents.
Edit intent: clarity
Original:  Characteristics of the resistive networks and p-bits are modeled in SPICE to perform a circuit-level simulation , which investigates the performance, area, and power consumption tradeoffs of the weighted array.
Revised:  Characteristics of the resistive networks and p-bits are modeled in SPICE to perform a circuit-level simulation investigating the performance, area, and power consumption tradeoffs of the weighted array.
Edit intent: coherence
Original:  In the application-level simulation, an R-DBN is implemented in MATLAB for digit recognition using the extracted device and circuit behavioral models.
Revised:  In the application-level simulation, a DBN is implemented in MATLAB for digit recognition using the extracted device and circuit behavioral models.
Edit intent: clarity
Original:  The MNIST data set is used to assess the accuracy of the R-DBN using 100 to 5,000 training images for five distinct network topologies.
Revised:  The MNIST data set is used to assess the accuracy of the DBN using 5,000 training images for five distinct network topologies.
Edit intent: clarity
Original:  The results indicate that a baseline error rate of 36.8\% for a 784x10 R-DBN trained by 100 samples can be reduced to only 3.7\% using a 784x800x800x10 R-DBN trained by 5,000 input samples.
Revised:  The results indicate that a baseline error rate of 36.8\% for a 784x10 DBN trained by 100 samples can be reduced to only 3.7\% using a 784x800x800x10 R-DBN trained by 5,000 input samples.
Edit intent: fluency
Original:  The results indicate that a baseline error rate of 36.8\% for a 784x10 R-DBN trained by 100 samples can be reduced to only 3.7\% using a 784x800x800x10 R-DBN trained by 5,000 input samples.
Revised:  The results indicate that a baseline error rate of 36.8\% for a 784x10 R-DBN trained by 100 samples can be reduced to only 3.7\% using a 784x800x800x10 DBN trained by 5,000 input samples.
Edit intent: clarity
Original:  Finally, power dissipation and accuracy tradeoffs for probabilistic computing mechanisms using resistive devices are identified.
Revised:  Finally, Power dissipation and accuracy tradeoffs for probabilistic computing mechanisms using resistive devices are identified.
Edit intent: fluency
Original:  Firstly, we propose a novel text search algorithm using a inverse filtering mechanism that is very efficient for label based item search . Secondly, we adopt the Bayesian network to implement the user interest prediction for an improved personalized search .
Revised:  Firstly, we propose a novel text search algorithm using an inverse filtering mechanism that is very efficient for label based item search . Secondly, we adopt the Bayesian network to implement the user interest prediction for an improved personalized search .
Edit intent: fluency
Original:  Firstly, we propose a novel text search algorithm using a inverse filtering mechanism that is very efficient for label based item search . Secondly, we adopt the Bayesian network to implement the user interest prediction for an improved personalized search .
Revised:  Firstly, we propose a novel text search algorithm using a inverse filtering mechanism that improves the efficiency . Secondly, we adopt the Bayesian network to implement the user interest prediction for an improved personalized search .
Edit intent: clarity