wanyu/IteraTeR_v2 huggingface dataset:
Original:  In particular we show that such Hermite subdivision operators admit d factorizations with respect to the Gregory operators: a new sequence of operators we define using Stirling numbers and Gregory coefficients.
Revised:  In particular we show that such Hermite subdivision operators admit d factorizations with respect to the Gregory operators: A new sequence of operators we define using Stirling numbers and Gregory coefficients.
Edit intent: fluency
Original:  We further prove that the d-th factorization provides a ' convergence from contractivity ' method for showing C^d-convergence of the associated Hermite subdivision scheme which deals with function values and first derivatives .
Revised:  We further prove that the d-th factorization provides a `` convergence from contractivity ' method for showing C^d-convergence of the associated Hermite subdivision scheme which deals with function values and first derivatives .
Edit intent: fluency
Original:  We further prove that the d-th factorization provides a ' convergence from contractivity ' method for showing C^d-convergence of the associated Hermite subdivision scheme which deals with function values and first derivatives .
Revised:  We further prove that the d-th factorization provides a ' convergence from contractivity '' method for showing C^d-convergence of the associated Hermite subdivision scheme which deals with function values and first derivatives .
Edit intent: fluency
Original:  We further prove that the d-th factorization provides a ' convergence from contractivity ' method for showing C^d-convergence of the associated Hermite subdivision scheme which deals with function values and first derivatives .
Revised:  We further prove that the d-th factorization provides a ' convergence from contractivity ' method for showing C^d-convergence of the associated Hermite subdivision scheme .
Edit intent: coherence
Original:  Our extended model allows studying the formatting of patterns and their temporal evolution also on the favourable and hostile substrates (environments) .
Revised:  Our extended model allows studying the formatting of patterns and their temporal evolution also on the favourable and hostile environments .
Edit intent: clarity
Original:  To our surprise  in the neutral environment, for the chosen inhibitor-value that ensures stable final patterns, the average size of final G-populations is lower than in the R-case.
Revised:  To our surprise , in the neutral environment, for the chosen inhibitor-value that ensures stable final patterns, the average size of final G-populations is lower than in the R-case.
Edit intent: fluency
Original:  In particular, above the critical inhibitor-values , their oscillatory behaviours are different.
Revised:  In particular, within the proper ranges of the critical values , their oscillatory behaviours are different.
Edit intent: clarity
Original:  When explicit expressions of the latter sums are available, this formula immediately provides explicit expressions of the former sums.
Revised:  When explicit expressions for the latter sums are available, this formula immediately provides explicit expressions of the former sums.
Edit intent: fluency
Original:  When explicit expressions of the latter sums are available, this formula immediately provides explicit expressions of the former sums.
Revised:  When explicit expressions of the latter sums are available, this formula immediately provides explicit expressions for the former sums.
Edit intent: fluency
Original:  such as the componen ts of an engine, the domains of a multiphysics problem, or solid bodies interacting under the influence of forces from surrounding fluids or other physical fields.
Revised:  such as the ts of an engine, the domains of a multiphysics problem, or solid bodies interacting under the influence of forces from surrounding fluids or other physical fields.
Edit intent: fluency
Original:  such as the componen ts of an engine, the domains of a multiphysics problem, or solid bodies interacting under the influence of forces from surrounding fluids or other physical fields.
Revised:  such as the componen components of an engine, the domains of a multiphysics problem, or solid bodies interacting under the influence of forces from surrounding fluids or other physical fields.
Edit intent: fluency
Original:   In the present paper  , we prove optimal order a~priori error estimate as well as optimal order estimates of the condition number  .
Revised:  In the present paper , we prove optimal order a~priori error estimates as well as optimal order estimates of the condition number .
Edit intent: fluency
Original:  In particular, we prove optimal order a~priori error estimates as well as optimal order estimates of the condition number.
Revised:  In particular, we prove optimal order a priori error estimates as well as optimal order estimates of the condition number.
Edit intent: fluency
Original: In this work, we aim to answer the question- what triggers cooperative behaviour in the thermodynamic limit by taking recourse to the Public goods game.
Revised: In this work, we aim to answer the question: what triggers cooperative behaviour in the thermodynamic limit by taking recourse to the Public goods game.
Edit intent: fluency
Original: In this work, we aim to answer the question- what triggers cooperative behaviour in the thermodynamic limit by taking recourse to the Public goods game.
Revised: In this work, we aim to answer the question- what triggers cooperative behavior in the thermodynamic limit by taking recourse to the Public goods game.
Edit intent: fluency
Original:  Using the idea of mapping the  Ising model Hamiltonian  to payoffs in  game theory we calculate the Magnetisation of a game in the thermodynamic limit.
Revised:  Using the idea of mapping the Ising model Hamiltonian to payoffs in the game theory we calculate the Magnetisation of a game in the thermodynamic limit.
Edit intent: fluency
Original:  Using the idea of mapping the  Ising model Hamiltonian  to payoffs in  game theory we calculate the Magnetisation of a game in the thermodynamic limit.
Revised:  Using the idea of mapping the Ising model Hamiltonian to payoffs in game theory we calculate the Magnetisation of the game in the thermodynamic limit.
Edit intent: fluency
Original:  We observe that punishment acts as an external field for the two player Public goods game triggering cooperation  , while cost can be a trigger for defection or suppressing cooperation .
Revised:  We observe that punishment acts as an external field for the two player Public goods game triggering cooperation , while cost can be a trigger for suppressing cooperation or free riding .
Edit intent: clarity
Original:  Finally, reward also acts as a trigger for cooperation while the role of inverse temperature (fluctuations in choices) remains ambiguous .
Revised:  Finally, reward also acts as a trigger for providing while the role of inverse temperature (fluctuations in choices) remains ambiguous .
Edit intent: clarity
Original: Zhou  Smith (2017) investigate different multi-species harvesting scenarios in a simple Holling-Tanner model.
Revised: Zhou and Smith (2017) investigate different multi-species harvesting scenarios in a simple Holling-Tanner model.
Edit intent: clarity
Original: Zhou  Smith (2017) investigate different multi-species harvesting scenarios in a simple Holling-Tanner model.
Revised: Zhou Smith (2017) investigate different multi-species harvesting scenarios using a simple Holling-Tanner model.
Edit intent: fluency
Original: A k-bend path is a rectilinear curve made up of  k + 1 line segments.
Revised: A is a rectilinear curve made up of k + 1 line segments.
Edit intent: clarity
Original:  A B_k-VPG representation of a graph is a collection of k-bend paths such that each path in the collection represents a vertex of the graph and two such paths intersect if and only if the vertices they represent are adjacent in the graph.
Revised:  A B_k-VPG representation of a graph is a collection of k-bend paths such that each path in the collection represents a vertex of the graph and two such paths intersect if and only if the vertices they represent are adjacent in the graph.
Edit intent: fluency
Original:  The graphs that have a B_k-VPG representation are called B_k-VPG graphs .
Revised:  The graphs that have a B_k-VPG representation are called .
Edit intent: clarity
Original:  ({wg 2012}) asking whether B_k-VPG-chordal \subsetneq B_{k+1}-VPG-chordal for all k \in N , where B_k-VPG denotes the class of graphs with bend number at most k.
Revised:  ({wg 2012}) who asked whether B_k-VPG-chordal \subsetneq B_{k+1}-VPG-chordal for all k \in N , where B_k-VPG denotes the class of graphs with bend number at most k.
Edit intent: fluency
Original:  We also prove that for all t \in N, B_t-VPG-Forb(C_{\geq 5}) \subsetneq B_{4t+29}-VPG-Forb(C_{\geq 5})  where Forb(C_{\geq 5}) denotes the family of graphs that does not contain induced cycles of length greater than 4.
Revised:  We also prove that for all t \in N, B_t-VPG-Forb(C_{\geq 5}) \subsetneq B_{4t+29}-VPG-Forb(C_{\geq 5}) , where Forb(C_{\geq 5}) denotes the family of graphs that does not contain induced cycles of length greater than 4.
Edit intent: fluency
Original:  Furthermore, we show that  PB_t-VPG-split \subsetneq PB_{36t+80}-VPG-split . for all t \in \mathbb{N , where PB_t-VPG denotes the class of graphs with proper bend number at most t . In this paper, we study the relationship between poset dimension and its bend number.
Revised:  Furthermore, we show that for all t \in \mathbb{N PB_t-VPG-split \subsetneq PB_{36t+80}-VPG-split . for all t \in \mathbb{N , where PB_t-VPG denotes the class of graphs with proper bend number at most t . In this paper, we study the relationship between poset dimension and its bend number.
Edit intent: fluency
Original:  Furthermore, we show that  PB_t-VPG-split \subsetneq PB_{36t+80}-VPG-split . for all t \in \mathbb{N , where PB_t-VPG denotes the class of graphs with proper bend number at most t . In this paper, we study the relationship between poset dimension and its bend number.
Revised:  Furthermore, we show that PB_t-VPG-split \subsetneq PB_{36t+80}-VPG-split , where PB_t-VPG denotes the class of graphs with proper bend number at most t . In this paper, we study the relationship between poset dimension and its bend number.
Edit intent: coherence
Original:  Cohen et al. (%DIFDELCMD < {%%% \textsc{order 2015 ) asked for examples of cocomparability graphs with low bend number and high poset dimension.
Revised:  Cohen et al. (%DIFDELCMD < {%%% \textsc{ ) asked for examples of cocomparability graphs with low bend number and high poset dimension.
Edit intent: clarity
Original: There exist many zero quantized discrete cosine transform (QDCT) coefficients in transform domain for video compression standards, such as H.264/ AVC. Besides, the modification, i. e., increasing or decreasing by 1 on zero QDCT coefficients of high frequency area, has an insignificant effect on visual quality of H.264/ AVC video.
Revised:  H.264/ AVC. Besides, the modification, i. e., increasing or decreasing by 1 on zero QDCT coefficients of high frequency area, has an insignificant effect on visual quality of H.264/ AVC video.
Edit intent: coherence
Original: We show that selecting a fixed precision for all activations in Convolutional Neural Networks, even if that precision is different per layer, amounts to worst case design.
Revised: We show that selecting a fixed precision for all values in Convolutional Neural Networks, even if that precision is different per layer, amounts to worst case design.
Edit intent: clarity
Original:  We show that much lower precisions can be used , if we could target the common case instead by tailoring the precision at a much finer granularity than that of a layer.
Revised:  We show that much lower precisions can be used if we could target the common case instead by tailoring the precision at a much finer granularity than that of a layer.
Edit intent: fluency
Original:   We propose Dynamic Prediction Reduction (DPRed)  where hardware on-the-fly detects the precision activations need and at a much finer granularity than a whole layer.
Revised:  We propose Dynamic Prediction Reduction (DPRed) , where hardware on-the-fly detects the precision activations need and at a much finer granularity than a whole layer.
Edit intent: fluency
Original:   We propose Dynamic Prediction Reduction (DPRed)  where hardware on-the-fly detects the precision activations need and at a much finer granularity than a whole layer.
Revised:  We propose Dynamic Prediction Reduction (DPRed) where hardware on-the-fly detects the precision activations need at a much finer granularity than a whole layer.
Edit intent: coherence
Original:  We also consider a lower cost variant that supports only even precision widths which offers better  energy efficiency.
Revised:  Finally, we consider a lower cost variant that supports only even precision widths which offers better energy efficiency.
Edit intent: coherence
Original: We show that selecting a fixed precision for all values in Convolutional Neural Networks, even if that precision is different per layer, amounts to worst case design.
Revised: We show that selecting a fixed precision for all values in Convolutional Neural Networks, even if that data type is different per layer, amounts to worst case design.
Edit intent: clarity
Original:  We show that much lower precisions can be used if we could target the common case instead by tailoring the precision at a much finer granularity than that of a layer.
Revised:  Much shorter data types can be used if we could target the common case instead by tailoring the precision at a much finer granularity than that of a layer.
Edit intent: clarity
Original:  We show that much lower precisions can be used if we could target the common case instead by tailoring the precision at a much finer granularity than that of a layer.
Revised:  We show that much lower precisions can be used if we target the common case instead by tailoring the precision at a much finer granularity than that of a layer.
Edit intent: clarity
Original:  We show that much lower precisions can be used if we could target the common case instead by tailoring the precision at a much finer granularity than that of a layer.
Revised:  We show that much lower precisions can be used if we could target the common case by adjusting the precision at a much finer granularity than that of a layer.
Edit intent: clarity
Original:  We propose Dynamic Prediction Reduction (DPRed), where hardware on-the-fly detects the precision activations need at a much finer granularity than a whole layer.
Revised:  We propose Dynamic Precision Reduction (DPRed), where hardware on-the-fly detects the precision activations need at a much finer granularity than a whole layer.
Edit intent: fluency
Original:  The evaluation over DARPA'98 dataset demonstrates that the proposed approach is better than the existing solutions as it provides 99.97 \ detection rate for anomalous class.
Revised:  The evaluation over DARPA'98 dataset demonstrates that the proposed approach is better than the existing solutions as it provides 99.97 \% detection rate for anomalous class.
Edit intent: clarity
Original:  We also provide a quantitative analysis of second-order stationary points for this problem , and show that with a certain tweak to the architecture, training the network with standard stochastic gradient descent achieves an objective value no worse than any fixed linear predictor.
Revised:  We also provide a quantitative analysis of second-order stationary points for this problem . Finally, we show that with a certain tweak to the architecture, training the network with standard stochastic gradient descent achieves an objective value no worse than any fixed linear predictor.
Edit intent: coherence
Original:  We also provide a quantitative analysis of second-order stationary points for this problem , and show that with a certain tweak to the architecture, training the network with standard stochastic gradient descent achieves an objective value no worse than any fixed linear predictor.
Revised:  We also provide a quantitative analysis of second-order stationary points for this problem , and show that with a certain tweak to the architecture, training the network with standard stochastic gradient descent achieves an objective value close or better than any linear predictor.
Edit intent: clarity
Original:  In this paper, we rigorously prove that arbitrarily deep, nonlinear ResNets indeed exhibit this behavior, in the sense that the optimization landscape contains no local minima with value above what can be obtained with a linear predictor (namely a 1-layer network).
Revised:  In this paper, we rigorously prove that arbitrarily deep, nonlinear residual units indeed exhibit this behavior, in the sense that the optimization landscape contains no local minima with value above what can be obtained with a linear predictor (namely a 1-layer network).
Edit intent: clarity
Original:  The purpose of this paper is to explore the impact of the wireless traffic, which fluctuates violently both spatially and temporally, on the performance of the wireless networks.
Revised:  The purpose of this paper is to explore the impact of the wireless traffic, which fluctuates both spatially and temporally, on the performance of the wireless networks.
Edit intent: clarity
Original:  The numerical results indicate that although the fluctuations of traffic when the users are clustered, reflected by the variance of total arrival rate , is much fiercer than that when the users are uniformly distributed, the stability performance is much better.
Revised:  The numerical results indicate that although the fluctuation of traffic ( reflected by the variance of total arrival rate , is much fiercer than that when the users are uniformly distributed, the stability performance is much better.
Edit intent: clarity
Original:  The numerical results indicate that although the fluctuation of traffic (reflected by the variance of total arrival rate) when the users are clustered is much fiercer than that when the users are uniformly distributed, the stability performance is much better .
Revised:  The numerical results indicate that although the fluctuation of traffic (reflected by the variance of total arrival rate) when the users are clustered is much fiercer than that when the users are uniformly distributed, the unstable probability is smaller .
Edit intent: clarity
Original: Independent samples from an unknown probability distribution \mathbf{p \bf  on a domain of size k are distributed across n players, with each player holding one sample.
Revised: Independent samples from an unknown probability distribution \bf on a domain of size k are distributed across n players, with each player holding one sample.
Edit intent: clarity
Original:  Each player can communicate \ell bits to a central referee in a simultaneous message passing (SMP) model of communication to help the referee infer a property of the unknown \mathbf{p.
Revised:  Each player can communicate \ell bits to a central referee in a simultaneous message passing model of communication to help the referee infer a property of the unknown \mathbf{p.
Edit intent: clarity
Original:  Each player can communicate \ell bits to a central referee in a simultaneous message passing (SMP) model of communication to help the referee infer a property of the unknown \mathbf{p.
Revised:  Each player can communicate \ell bits to a central referee in a simultaneous message passing (SMP) model of communication to help the referee infer a property of the unknown .
Edit intent: coherence
Original:  It turns out that Shearer's bound is generally not tight for variable version LLL (VLLL) he2017variable .
Revised:  It turns out that Shearer's bound is generally not tight for variable version LLL (VLLL) he2017variable .
Edit intent: fluency
Original:  Our result also } shows the tightness of Gily{\'e}n and Sattath's algorithm }\hspace{0pt} } , and implies that the lattice gas partition function fully characterizes quantum satisfiability for almost all Hamiltonians with large enough qudits }\hspace{0pt} } . Commuting LLL (CLLL), LLL for commuting local Hamiltonians which are widely studied in  literature, is also investigated here.
Revised:  Our result also } shows the tightness of Gily{\'e}n and Sattath's algorithm }\hspace{0pt} } , and implies that the lattice gas partition function fully characterizes quantum satisfiability for almost all Hamiltonians with large enough qudits }\hspace{0pt} } . Commuting LLL (CLLL), LLL for commuting local Hamiltonians which are widely studied in the literature, is also investigated here.
Edit intent: fluency
Original:  We prove that the tight regions of CLLL and QLLL are generally different .
Revised:  We prove that the tight regions of CLLL and QLLL are different in general .
Edit intent: fluency
Original:  Thus, the efficient region of algorithms for CLLL can go beyond shearer 's bound.
Revised:  Thus, the efficient region of algorithms for CLLL can go beyond Shearer 's bound.
Edit intent: fluency
Original:  Over the last decades, the algorithmic aspect of LLL has also attracted lots of attention in theoretical computer science ~\mbox{ moser2010constructive,kolipaka2011moser,harvey2015algorithmic .
Revised:  Over the last decades, the algorithmic aspect of LLL has also attracted lots of attention in theoretical computer science .
Edit intent: coherence
Original:  A tight criterion under which the abstract version LLL (ALLL) holds was given by Shearer ~\mbox{ shearer1985problem .
Revised:  A tight criterion under which the abstract version LLL (ALLL) holds was given by Shearer .
Edit intent: clarity
Original:  It turns out that Shearer's bound is generally not tight for variable version LLL (VLLL) ~\mbox{ he2017variable .
Revised:  It turns out that Shearer's bound is generally not tight for variable version LLL (VLLL) .
Edit intent: coherence
Original:  \mbox{ ambainis2012quantum introduced a quantum version LLL (QLLL), which was then shown to be powerful for quantum satisfiability problem.
Revised:  introduced a quantum version LLL (QLLL), which was then shown to be powerful for quantum satisfiability problem.
Edit intent: coherence
Original:  ~\mbox{ pnas,Morampudi2018Many .
Revised:  .
Edit intent: coherence
Original:  Our result also shows the tightness of Gily{\'e}n and Sattath's algorithm \mbox{ gilyen2016preparing , and implies that the lattice gas partition function fully characterizes quantum satisfiability for almost all Hamiltonians with large enough qudits ~\mbox{ pnas . Commuting LLL (CLLL), LLL for commuting local Hamiltonians which are widely studied in the literature, is also investigated here.
Revised:  Our result also shows the tightness of Gily{\'e}n and Sattath's algorithm , and implies that the lattice gas partition function fully characterizes quantum satisfiability for almost all Hamiltonians with large enough qudits ~\mbox{ pnas . Commuting LLL (CLLL), LLL for commuting local Hamiltonians which are widely studied in the literature, is also investigated here.
Edit intent: clarity
Original:  Our result also shows the tightness of Gily{\'e}n and Sattath's algorithm \mbox{ gilyen2016preparing , and implies that the lattice gas partition function fully characterizes quantum satisfiability for almost all Hamiltonians with large enough qudits ~\mbox{ pnas . Commuting LLL (CLLL), LLL for commuting local Hamiltonians which are widely studied in the literature, is also investigated here.
Revised:  Our result also shows the tightness of Gily{\'e}n and Sattath's algorithm \mbox{ gilyen2016preparing , and implies that the lattice gas partition function fully characterizes quantum satisfiability for almost all Hamiltonians with large enough qudits . Commuting LLL (CLLL), LLL for commuting local Hamiltonians which are widely studied in the literature, is also investigated here.
Edit intent: clarity
Original: Consider the following process on a network: Each agent initially holds either opinion emph blue%DIFDELCMD < } %%% orred ;
Revised: Consider the following process on a network: Each agent initially holds either opinion blue%DIFDELCMD < } %%% orred ;
Edit intent: fluency