wanyu/IteraTeR_v2 huggingface dataset:
Original:  The idea is to derive  from the high-dimensional input matrix a smaller matrix , which is then used to efficiently compute the dynamic modes and eigenvalues.
Revised:  The idea is to derive from the high-dimensional data , which is then used to efficiently compute the dynamic modes and eigenvalues.
Edit intent: clarity
Original:  The algorithm is presented in a modular probabilistic framework, and the approximation quality can be controlled via oversampling , and power iterations  .
Revised:  The algorithm is presented in a modular probabilistic framework, and the approximation quality can be controlled via oversampling and power iterations .
Edit intent: fluency
Original:  The effectiveness of the resulting randomized DMD (rDMD) algorithm is demonstrated on several benchmark examples of increasing complexity, providing an accurate and efficient approach to extract spatiotemporal coherent structures from big data in a framework that scales with the intrinsic rank of the data, rather than the ambient measurement dimension  .
Revised:  The effectiveness of the resulting randomized DMD algorithm is demonstrated on several benchmark examples of increasing complexity, providing an accurate and efficient approach to extract spatiotemporal coherent structures from big data in a framework that scales with the intrinsic rank of the data, rather than the ambient measurement dimension .
Edit intent: clarity
Original:  Above this, not much was known, until Salvati showed recently that the word problem of Z^2 is  multiple context-free  , giving first such example.
Revised:  Above this, not much was known, until Salvati showed recently that the word problem of Z^2 is a multiple context-free , giving first such example.
Edit intent: fluency
Original:  In this paper we count the number of closed affine %DIFDELCMD < \lambdaterms %%%  of size n, closed linear \lambda-terms of size n, affine \beta-normal forms of size n and linear \beta-normal forms of ise n, for different ways of measuring the size of \lambda-terms.
Revised:  In this paper we count the number of closed affine %DIFDELCMD < \lambdaterms %%% \lambda-terms of size n, closed linear \lambda-terms of size n, affine \beta-normal forms of size n and linear \beta-normal forms of ise n, for different ways of measuring the size of \lambda-terms.
Edit intent: fluency
Original:  The process is a Markov chain, which is formulated in both a continuous-time and a discrete-time version .
Revised:  The process arises in population genetics and describes the ancestry of the genetic material of individuals in a population experiencing recombination .
Edit intent: clarity
Original:  In discrete time, however, dependencies within the fragments , which get lost over time, make it difficult to obtain analogous explicit results .
Revised:  In discrete time, however, dependencies. Dependencies within the fragments , which get lost over time, make it difficult to obtain analogous explicit results .
Edit intent: coherence
Original:  In discrete time, however, dependencies within the fragments , which get lost over time, make it difficult to obtain analogous explicit results .
Revised:  In discrete time, however, dependencies within the fragments make it difficult to obtain analogous explicit results .
Edit intent: clarity
Original:  The fragmentation process arises in population genetics and describes the ancestry of the genetic material of individuals in a population experiencing recombination
Edit intent: coherence
Original:  In this paper, we present a polyhedral study of 2-level polytopes arising in combinatorial settings.
Revised:  In this paper, we present a study of some 2-level polytopes arising in combinatorial settings.
Edit intent: clarity
Original:  For all the known (to the best of our knowledge) such polytopes P, we show that v(P) .f (P) is upper bounded by d2 ^(d+1)  .
Revised:  Our first contribution is proving that v(P) .f (P) is upper bounded by d2 ^(d+1) .
Edit intent: coherence
Original:  For all the known (to the best of our knowledge) such polytopes P, we show that v(P) .f (P) is upper bounded by d2 ^(d+1)  .
Revised:  For all the known (to the best of our knowledge) such polytopes P, we show that v(P) *f (P) is upper bounded by d2 ^(d+1) .
Edit intent: fluency
Original:  Whether this holds for all 2-level polytopes was asked in [Bohn et al., ESA 2015], where experimental results  showed it true up to dimension 6.
Revised:  Whether this holds for all 2-level polytopes was asked in [Bohn et al., ESA 2015], and experimental results from showed it true up to dimension 6.
Edit intent: coherence
Original:  The key to most of our proofs is an understanding of the combinatorial structures underlying those polytopes .
Revised:  The key to most of our proofs is a deeper understanding of the combinatorial structures underlying those polytopes .
Edit intent: clarity
Original:  The key to most of our proofs is an understanding of the combinatorial structures underlying those polytopes .
Revised:  The key to most of our proofs is an understanding of the relations among those polytopes and their underlying combinatorial structures .
Edit intent: clarity
Original: We obtain optimal strategies for the allocation of influence budget across multiple channels and across time for an external influencer, e. g., a political campaign, seeking to maximize its effect on an election given a network of agents with linear consensus-seeking opinion dynamics.
Revised: We analyze optimal strategies for the allocation of influence budget across multiple channels and across time for an external influencer, e. g., a political campaign, seeking to maximize its effect on an election given a network of agents with linear consensus-seeking opinion dynamics.
Edit intent: clarity
Original: We obtain optimal strategies for the allocation of influence budget across multiple channels and across time for an external influencer, e. g., a political campaign, seeking to maximize its effect on an election given a network of agents with linear consensus-seeking opinion dynamics.
Revised: We obtain optimal strategies for the allocation of a finite budget that can be invested in different advertising channels over time with the objective of influencing social opinions in a network of individuals. In our analysis, we consider both exogenous influence mechanisms, such as advertising campaigns, as well as endogenous mechanisms of social influence, such as word-of-mouth and peer-pressure, which are modeled using diffusion dynamics.
Edit intent: clarity
Original:  We show that for a general set of objective functions, the optimal influence strategy at every time uses all channels at either their maximum rate or not at all .
Revised:  We show that for a broad family of objective functions, the optimal influence strategy at every time uses all channels at either their maximum rate or not at all .
Edit intent: clarity
Original:  Furthermore, we prove that the number of switches between these extremes is bounded above both by a term that is typically much smaller than the number of agents.
Revised:  Furthermore, we prove that the number of switches between these extremes is bounded above by a term that is typically much smaller than the number of agents.
Edit intent: clarity
Original:  We also show that  at the beginning  , the total cost-adjusted reach of a channel determines its relative value , while targeting matters more closer to election time .
Revised:  We also show that , at the beginning , the total cost-adjusted reach of a channel determines its relative value , while targeting matters more closer to election time .
Edit intent: fluency
Original:  We also show that  at the beginning  , the total cost-adjusted reach of a channel determines its relative value , while targeting matters more closer to election time .
Revised:  We also show that at the beginning of the campaign , the total cost-adjusted reach of a channel determines its relative value , while targeting matters more closer to election time .
Edit intent: clarity
Original:  We demonstrate that the optimal influence structures are easily computable in several practical cases .
Revised:  We demonstrate that the optimal influence strategies are easily computable in several practical cases .
Edit intent: clarity
Original:  We explicitly characterize the optimal controls for the case of linear objective functions via a closed form.
Revised:  We explicitly characterize the optimal controls for the case of linear objective functions in closed form.
Edit intent: clarity
Original:  Finally, we see that  in the canonical election example , identifying late-deciders approximately determines the optimal campaign resource allocation strategy .
Revised:  Finally, we see that , in the canonical election example , identifying late-deciders approximately determines the optimal campaign resource allocation strategy .
Edit intent: coherence
Original:  Finally, we see that  in the canonical election example , identifying late-deciders approximately determines the optimal campaign resource allocation strategy .
Revised:  Finally, we see that in the canonical example of designing an election campaign , identifying late-deciders approximately determines the optimal campaign resource allocation strategy .
Edit intent: clarity
Original:  Finally, we see that  in the canonical election example , identifying late-deciders approximately determines the optimal campaign resource allocation strategy .
Revised:  Finally, we see that in the canonical election example , identifying late-deciders is a critical component in the optimal design .
Edit intent: clarity
Original:  In this paper, we propose a two-step framework (namely, group scissor ) to scale NCS designs to big neural networks.
Revised:  In this paper, we propose a two-step framework (namely, group scissor ) to scale NCS designs to big neural networks.
Edit intent: fluency
Original:  The first step is rank clipping , which integrates low-rank approximation into the training to reduce total crossbar area.
Revised:  The first step is rank clipping , which integrates low-rank approximation into the training to reduce total crossbar area.
Edit intent: fluency
Original:  The second step is group connection deletion , which structurally prunes connections to reduce routing congestion between crossbars.
Revised:  The second step is group connection deletion , which structurally prunes connections to reduce routing congestion between crossbars.
Edit intent: fluency
Original:  Tested on convolutional neural networks of LeNet on MNIST database and ConvNet on CIFAR-10 database, our experiments show significant reduction of crossbar area and routing area in NCS designs.
Revised:  Tested on convolutional neural networks of LeNet on MNIST database and ConvNet on CIFAR-10 database, our experiments show significant reduction of crossbar area and routing area in NCS designs.
Edit intent: fluency
Original:  Without accuracy loss, rank clipping reduces total crossbar area to 13.62\\%DIF < and 51.81\\% in the NCS designs ofLeNet andConvNet , respectively.
Revised:  Without accuracy loss, rank clipping reduces total crossbar area to 13.62\\%DIF < and 51.81\\% in the LeNet andConvNet , respectively.
Edit intent: clarity
Original:  Without accuracy loss, rank clipping reduces total crossbar area to 13.62\\%DIF < and 51.81\\% in the NCS designs ofLeNet andConvNet , respectively.
Revised:  Without accuracy loss, rank clipping reduces total crossbar area to 13.62\\%DIF < and 51.81\\% in the NCS designs of andConvNet , respectively.
Edit intent: fluency
Original:  Without accuracy loss, rank clipping reduces total crossbar area to 13.62\\%DIF < and 51.81\\% in the NCS designs ofLeNet andConvNet , respectively.
Revised:  Without accuracy loss, rank clipping reduces total crossbar area to 13.62\\%DIF < and 51.81\\% in the NCS designs ofLeNet ConvNet , respectively.
Edit intent: fluency
Original:  Without accuracy loss, rank clipping reduces total crossbar area to 13.62\\%DIF < and 51.81\\% in the NCS designs ofLeNet andConvNet , respectively.
Revised:  Without accuracy loss, rank clipping reduces total crossbar area to 13.62\\%DIF < and 51.81\\% in the NCS designs ofLeNet and , respectively.
Edit intent: clarity
Original:  Following rank clipping, group connection deletion further reduces the routing area of LeNet and\textit{ConvNet to 8.1\\% and 52.06\\%, respectively.
Revised:  Following rank clipping, group connection deletion further reduces the routing area of and\textit{ConvNet to 8.1\\% and 52.06\\%, respectively.
Edit intent: fluency
Original:  Following rank clipping, group connection deletion further reduces the routing area of LeNet and\textit{ConvNet to 8.1\\% and 52.06\\%, respectively.
Revised:  Following rank clipping, group connection deletion further reduces the routing area of LeNet \textit{ConvNet to 8.1\\% and 52.06\\%, respectively.
Edit intent: fluency
Original:  Models of this neural network activity will necessarily increase in size and complexity, thus increasing the computational cost of simulating them and new challenges in analyzing them.
Revised:  Models of this neural network activity will necessarily increase in size and complexity, thus increasing the computational cost of simulating them and the challenge of analyzing them.
Edit intent: clarity
Original:  Here we present a novel approximation method to approximate the activity and firing statistics of a general firing rate network model (of Wilson-Cowan type) subject to noisy correlated background inputs.
Revised:  Here we present a novel method to approximate the activity and firing statistics of a general firing rate network model (of Wilson-Cowan type) subject to noisy correlated background inputs.
Edit intent: clarity
Original: Managing micro-tasks on crowdsourcing marketplaces involves balancing conflicting objectives -- the quality of work, total cost incurred  and time to completion.
Revised: Managing micro-tasks on crowdsourcing marketplaces involves balancing conflicting objectives -- the quality of work, total cost incurred , and time to completion.
Edit intent: fluency
Original:  Previous agents have focused on cost-quality, or cost-time tradeoffs, limiting their real-world applicability.
Revised:  Previous control agents have mostly focused on cost-quality, or cost-time tradeoffs, limiting their real-world applicability.
Edit intent: clarity
Original:  We demonstrate that Octopus  outperforms existing state-of-the-art approaches in simulation and experiments with real data, demonstrating its superior performance .
Revised:  We demonstrate that Octopus outperforms existing state-of-the-art approaches on real experiments .
Edit intent: clarity
Original:  We also deploy Octopus on Amazon Mechanical Turk to establish its ability to manage tasks in a real-world , dynamic setting.
Revised:  We also deploy Octopus on Amazon Mechanical Turk , showing its ability to manage tasks in a real-world , dynamic setting.
Edit intent: coherence
Original:  We also deploy Octopus on Amazon Mechanical Turk to establish its ability to manage tasks in a real-world , dynamic setting.
Revised:  We also deploy Octopus on Amazon Mechanical Turk to establish its ability to manage tasks in a real-world dynamic setting.
Edit intent: fluency
Original: We propose that the brain performs approximate probabilistic inference using nonlinear recurrent processing in redundant population codes.
Revised: It is widely believed that the brain performs approximate probabilistic inference using nonlinear recurrent processing in redundant population codes.
Edit intent: clarity
Original:  Electrophysiological recordings provide detailed spiking information about neurons but have traditionally been confined to a particular region or layer of cortex.
Revised:  Electrophysiological recordings provide detailed information about neural spiking but have traditionally been confined to a particular region or layer of cortex.
Edit intent: fluency
Original:  Here , we develop a novel theoretical framework that relies on efficiently calculating the first and second order statistics in a multi-population firing rate model .
Revised:  Here we develop new theoretical methods to study interactions between and within two brain regions, based on experimental measurements of spiking activity simultaneously recorded from the two regions. By systematically comparing experimentally-obtained spiking statistics to (efficiently computed) model spike rate statistics, we identify regions in model parameter space that are consistent with the experimental data .
Edit intent: clarity
Original:  We apply this method to determine qualitative relationships between important network connections in the rat olfactory system, when the model is constrained by data from simultaneous dual micro-electrode array in vivo recordings from two distinct regions , the olfactory bulb (OB) and anterior piriform cortex (PC).
Revised:  We apply our new technique to dual micro-electrode array in vivo recordings from two distinct regions , the olfactory bulb (OB) and anterior piriform cortex (PC).
Edit intent: clarity
Original:  We apply this method to determine qualitative relationships between important network connections in the rat olfactory system, when the model is constrained by data from simultaneous dual micro-electrode array in vivo recordings from two distinct regions , the olfactory bulb (OB) and anterior piriform cortex (PC).
Revised:  We apply this method to determine qualitative relationships between important network connections in the rat olfactory system, when the model is constrained by data from simultaneous dual micro-electrode array in vivo recordings from two distinct regions : olfactory bulb (OB) and anterior piriform cortex (PC).
Edit intent: fluency
Original:  In particular, the model predicts that: i) inhibition within the afferent region (OB) has to be less than the inhibition in PC, ii) excitation from PC to OB is often stronger than excitation from OB to PC, iii) excitation from PC to OB and inhibition within PC have to both be relatively strong compared to presynaptic inputs from OB.
Revised:  Our analysis predicts that: i) inhibition within the afferent region (OB) has to be less than the inhibition in PC, ii) excitation from PC to OB is often stronger than excitation from OB to PC, iii) excitation from PC to OB and inhibition within PC have to both be relatively strong compared to presynaptic inputs from OB.
Edit intent: clarity
Original:  In particular, the model predicts that: i) inhibition within the afferent region (OB) has to be less than the inhibition in PC, ii) excitation from PC to OB is often stronger than excitation from OB to PC, iii) excitation from PC to OB and inhibition within PC have to both be relatively strong compared to presynaptic inputs from OB.
Revised:  In particular, the model predicts that: i) inhibition within the afferent region (OB) has to be weaker than the inhibition in PC, ii) excitation from PC to OB is often stronger than excitation from OB to PC, iii) excitation from PC to OB and inhibition within PC have to both be relatively strong compared to presynaptic inputs from OB.
Edit intent: clarity
Original:  In particular, the model predicts that: i) inhibition within the afferent region (OB) has to be less than the inhibition in PC, ii) excitation from PC to OB is often stronger than excitation from OB to PC, iii) excitation from PC to OB and inhibition within PC have to both be relatively strong compared to presynaptic inputs from OB.
Revised:  In particular, the model predicts that: i) inhibition within the afferent region (OB) has to be less than the inhibition within PC, ii) excitation from PC to OB is often stronger than excitation from OB to PC, iii) excitation from PC to OB and inhibition within PC have to both be relatively strong compared to presynaptic inputs from OB.
Edit intent: fluency
Original:  In particular, the model predicts that: i) inhibition within the afferent region (OB) has to be less than the inhibition in PC, ii) excitation from PC to OB is often stronger than excitation from OB to PC, iii) excitation from PC to OB and inhibition within PC have to both be relatively strong compared to presynaptic inputs from OB.
Revised:  In particular, the model predicts that: i) inhibition within the afferent region (OB) has to be less than the inhibition in PC, ii) excitation from PC to OB is generally stronger than excitation from OB to PC, iii) excitation from PC to OB and inhibition within PC have to both be relatively strong compared to presynaptic inputs from OB.
Edit intent: clarity
Original:  These predictions are validated in a full spiking (leaky integrate-and-fire) neural network model of the OB-PC pathway that satisfies the many constraints from our experimental data.
Revised:  These predictions are validated in a spiking neural network model of the OB-PC pathway that satisfies the many constraints from our experimental data.
Edit intent: clarity
Original:  These predictions are validated in a full spiking (leaky integrate-and-fire) neural network model of the OB-PC pathway that satisfies the many constraints from our experimental data.
Revised:  These predictions are validated in a full spiking (leaky integrate-and-fire) neural network model of the OB--PC pathway that satisfies the many constraints from our experimental data.
Edit intent: fluency
Original: The emergent field of probabilistic numerics has thus far lacked rigorous statistical principals.
Revised: The emergent field of probabilistic numerics has thus far lacked clear statistical principals.
Edit intent: clarity
Original:  This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain Bayesian inverse problems , albeit problems that are non-standard .
Revised:  This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the Bayesian framework .
Edit intent: clarity
Original:  For general computation, a numerical approximation scheme is developed and its asymptotic convergence is established.
Revised:  For general computation, a numerical approximation scheme is proposed and its asymptotic convergence is established.
Edit intent: clarity
Original:  For general computation, a numerical approximation scheme is developed and its asymptotic convergence is established.
Revised:  For general computation, a numerical approximation scheme is developed and its asymptotic convergence established.
Edit intent: fluency
Original: We study the in-network computation of arbitrary functions whose computation schema is a complete binary tree, i. e., we assume that the network wants to compute a functionof K operands, each of which is available at a distinct node in the network, and rather than simply collecting the K operands at a single sink node and computing the function, we want to compute the function during the process of moving the data towards the sink.
Revised: We study in-network computation of arbitrary functions whose computation schema is a complete binary tree, i. e., we assume that the network wants to compute a functionof K operands, each of which is available at a distinct node in the network, and rather than simply collecting the K operands at a single sink node and computing the function, we want to compute the function during the process of moving the data towards the sink.
Edit intent: fluency
Original: We study the in-network computation of arbitrary functions whose computation schema is a complete binary tree, i. e., we assume that the network wants to compute a functionof K operands, each of which is available at a distinct node in the network, and rather than simply collecting the K operands at a single sink node and computing the function, we want to compute the function during the process of moving the data towards the sink.
Revised: We study the in-network computation on general network topologies. Specifically, we are given the description of a function, and a network with designated distinct nodes at which the operands of the function are made available, and a designated sink where the computed value of the function is to be consumed. We want to compute the function during the process of moving the data towards the sink.
Edit intent: clarity