wanyu/IteraTeR_v2 huggingface dataset:
Original:  Despite their appeal NTMs have a weakness that is caused by their sequential nature: they cannot be parallelized and are are hard to train due to their large depth when unfolded.
Revised:  Despite their appeal NTMs have a weakness that is caused by their sequential nature: they are not parallel and are are hard to train due to their large depth when unfolded.
Edit intent: clarity
Original: = span\,B_{n+1} with an inner product }%DIFDELCMD < \left<%%% \cdot,\cdot%DIFDELCMD < \right>%%% . A dual basis D_n for the basis B_n := B_{n+1 \setminus }%DIFDELCMD < \left\{%%% b_{n+1}%DIFDELCMD < \right\} %%% of the linear space \mathcal{B_{n} := span\,B_n with respect to the same inner product can be computed quickly using a new formula connecting the dual functions from D_{n+1} and D_n.
Revised: = span\,B_{n+1} with an inner product }%DIFDELCMD < \left<%%% %DIFDELCMD < \right>%%% . A dual basis D_n for the basis B_n := B_{n+1 \setminus }%DIFDELCMD < \left\{%%% b_{n+1}%DIFDELCMD < \right\} %%% of the linear space \mathcal{B_{n} := span\,B_n with respect to the same inner product can be computed quickly using a new formula connecting the dual functions from D_{n+1} and D_n.
Edit intent: fluency
Original: = span\,B_{n+1} with an inner product }%DIFDELCMD < \left<%%% \cdot,\cdot%DIFDELCMD < \right>%%% . A dual basis D_n for the basis B_n := B_{n+1 \setminus }%DIFDELCMD < \left\{%%% b_{n+1}%DIFDELCMD < \right\} %%% of the linear space \mathcal{B_{n} := span\,B_n with respect to the same inner product can be computed quickly using a new formula connecting the dual functions from D_{n+1} and D_n.
Revised: = span\,B_{n+1} with an inner product }%DIFDELCMD < \left<%%% \cdot,\cdot%DIFDELCMD < \right>%%% \setminus }%DIFDELCMD < \left\{%%% b_{n+1}%DIFDELCMD < \right\} %%% of the linear space \mathcal{B_{n} := span\,B_n with respect to the same inner product can be computed quickly using a new formula connecting the dual functions from D_{n+1} and D_n.
Edit intent: clarity
Original: = span\,B_{n+1} with an inner product }%DIFDELCMD < \left<%%% \cdot,\cdot%DIFDELCMD < \right>%%% . A dual basis D_n for the basis B_n := B_{n+1 \setminus }%DIFDELCMD < \left\{%%% b_{n+1}%DIFDELCMD < \right\} %%% of the linear space \mathcal{B_{n} := span\,B_n with respect to the same inner product can be computed quickly using a new formula connecting the dual functions from D_{n+1} and D_n.
Revised: = span\,B_{n+1} with an inner product }%DIFDELCMD < \left<%%% \cdot,\cdot%DIFDELCMD < \right>%%% . A dual basis D_n for the basis B_n := B_{n+1 \setminus }%DIFDELCMD < \left\{%%% }%DIFDELCMD < \right\} %%% of the linear space \mathcal{B_{n} := span\,B_n with respect to the same inner product can be computed quickly using a new formula connecting the dual functions from D_{n+1} and D_n.
Edit intent: clarity
Original: For every\varUpsilon k \in N_0, we consider graphs G where for every induced subgraphH of G, \Delta (H) \leq \chi (H)\varUpsilon -1 + k holds, where \Delta (H) is the maximum degree and \chi (H) is the chromatic number of the subgraph H. Let us call this family of graphs~%DIFDELCMD < \varUpsilon%%% _k. We give a finite forbidden induced subgraph characterization of%DIFDELCMD < \varUpsilon%%% _k for every k.
Revised: We provide a finite forbidden induced subgraph characterization for the graph class\varUpsilon k \in N_0, we consider graphs G where for every induced subgraphH of G, \Delta (H) \leq \chi (H)\varUpsilon -1 + k holds, where \Delta (H) is the maximum degree and \chi (H) is the chromatic number of the subgraph H. Let us call this family of graphs~%DIFDELCMD < \varUpsilon%%% _k. We give a finite forbidden induced subgraph characterization of%DIFDELCMD < \varUpsilon%%% _k for every k.
Edit intent: clarity
Original: For every\varUpsilon k \in N_0, we consider graphs G where for every induced subgraphH of G, \Delta (H) \leq \chi (H)\varUpsilon -1 + k holds, where \Delta (H) is the maximum degree and \chi (H) is the chromatic number of the subgraph H. Let us call this family of graphs~%DIFDELCMD < \varUpsilon%%% _k. We give a finite forbidden induced subgraph characterization of%DIFDELCMD < \varUpsilon%%% _k for every k.
Revised: For every\varUpsilon_k, for all k \in N_0, we consider graphs G where for every induced subgraphH of G, \Delta (H) \leq \chi (H)\varUpsilon -1 + k holds, where \Delta (H) is the maximum degree and \chi (H) is the chromatic number of the subgraph H. Let us call this family of graphs~%DIFDELCMD < \varUpsilon%%% _k. We give a finite forbidden induced subgraph characterization of%DIFDELCMD < \varUpsilon%%% _k for every k.
Edit intent: clarity
Original: For every\varUpsilon k \in N_0, we consider graphs G where for every induced subgraphH of G, \Delta (H) \leq \chi (H)\varUpsilon -1 + k holds, where \Delta (H) is the maximum degree and \chi (H) is the chromatic number of the subgraph H. Let us call this family of graphs~%DIFDELCMD < \varUpsilon%%% _k. We give a finite forbidden induced subgraph characterization of%DIFDELCMD < \varUpsilon%%% _k for every k.
Revised: For every\varUpsilon k \in N_0, which is defined as follows. A graph is in\varUpsilon -1 + k holds, where \Delta (H) is the maximum degree and \chi (H) is the chromatic number of the subgraph H. Let us call this family of graphs~%DIFDELCMD < \varUpsilon%%% _k. We give a finite forbidden induced subgraph characterization of%DIFDELCMD < \varUpsilon%%% _k for every k.
Edit intent: clarity
Original: For every\varUpsilon k \in N_0, we consider graphs G where for every induced subgraphH of G, \Delta (H) \leq \chi (H)\varUpsilon -1 + k holds, where \Delta (H) is the maximum degree and \chi (H) is the chromatic number of the subgraph H. Let us call this family of graphs~%DIFDELCMD < \varUpsilon%%% _k. We give a finite forbidden induced subgraph characterization of%DIFDELCMD < \varUpsilon%%% _k for every k.
Revised: For every\varUpsilon k \in N_0, we consider graphs G where for every induced subgraphH of G, \Delta (H) \leq \chi (H)\varUpsilon -1 + k holds, where \Delta is the maximum degree and \chi (H) is the chromatic number of the subgraph H. Let us call this family of graphs~%DIFDELCMD < \varUpsilon%%% _k. We give a finite forbidden induced subgraph characterization of%DIFDELCMD < \varUpsilon%%% _k for every k.
Edit intent: fluency
Original: For every\varUpsilon k \in N_0, we consider graphs G where for every induced subgraphH of G, \Delta (H) \leq \chi (H)\varUpsilon -1 + k holds, where \Delta (H) is the maximum degree and \chi (H) is the chromatic number of the subgraph H. Let us call this family of graphs~%DIFDELCMD < \varUpsilon%%% _k. We give a finite forbidden induced subgraph characterization of%DIFDELCMD < \varUpsilon%%% _k for every k.
Revised: For every\varUpsilon k \in N_0, we consider graphs G where for every induced subgraphH of G, \Delta (H) \leq \chi (H)\varUpsilon -1 + k holds, where \Delta (H) is the maximum degree and \chi is the chromatic number of the subgraph H. Let us call this family of graphs~%DIFDELCMD < \varUpsilon%%% _k. We give a finite forbidden induced subgraph characterization of%DIFDELCMD < \varUpsilon%%% _k for every k.
Edit intent: fluency
Original: For every\varUpsilon k \in N_0, we consider graphs G where for every induced subgraphH of G, \Delta (H) \leq \chi (H)\varUpsilon -1 + k holds, where \Delta (H) is the maximum degree and \chi (H) is the chromatic number of the subgraph H. Let us call this family of graphs~%DIFDELCMD < \varUpsilon%%% _k. We give a finite forbidden induced subgraph characterization of%DIFDELCMD < \varUpsilon%%% _k for every k.
Revised: For every\varUpsilon k \in N_0, we consider graphs G where for every induced subgraphH of G, \Delta (H) \leq \chi (H)\varUpsilon -1 + k holds, where \Delta (H) is the maximum degree and \chi (H) is the chromatic number of the subgraph %DIFDELCMD < \varUpsilon%%% _k. We give a finite forbidden induced subgraph characterization of%DIFDELCMD < \varUpsilon%%% _k for every k.
Edit intent: clarity
Original:  We compare these results with those given in  On bounding the difference between the maximum degree and the clique number, Graphs and Combinatorics 31(5) : 1689-1702 (2015)  , where we studied the graphs in which\varOmega for any induced subgraph H, \Delta (H) \leq \omega (H) -1 + k holds, where \omega (H) denotes the clique number of a graph.
Revised:  We compare these results with those given in On bounding the difference between the maximum degree and the clique number, Graphs and Combinatorics 31(5) , 1689-1702 (2015) , where we studied the graphs in which\varOmega for any induced subgraph H, \Delta (H) \leq \omega (H) -1 + k holds, where \omega (H) denotes the clique number of a graph.
Edit intent: fluency
Original:  We compare these results with those given in  On bounding the difference between the maximum degree and the clique number, Graphs and Combinatorics 31(5) : 1689-1702 (2015)  , where we studied the graphs in which\varOmega for any induced subgraph H, \Delta (H) \leq \omega (H) -1 + k holds, where \omega (H) denotes the clique number of a graph.
Revised:  We compare these results with those given in On bounding the difference between the maximum degree and the clique number, Graphs and Combinatorics 31(5) : 1689-1702 (2015) , where we studied the graph class\varOmega for any induced subgraph H, \Delta (H) \leq \omega (H) -1 + k holds, where \omega (H) denotes the clique number of a graph.
Edit intent: clarity
Original:  We compare these results with those given in  On bounding the difference between the maximum degree and the clique number, Graphs and Combinatorics 31(5) : 1689-1702 (2015)  , where we studied the graphs in which\varOmega for any induced subgraph H, \Delta (H) \leq \omega (H) -1 + k holds, where \omega (H) denotes the clique number of a graph.
Revised:  We compare these results with those given in On bounding the difference between the maximum degree and the clique number, Graphs and Combinatorics 31(5) : 1689-1702 (2015) , where we studied the graphs in which\varOmega for any induced subgraph H, \Delta (H) \leq \omega (H) -1 + k holds, where \omega denotes the clique number of a graph.
Edit intent: fluency
Original:  We find a nice characterization of this graph class in terms of \varOmega_k and \varUpsilon_k : We prove that a graph G is a neighborhood perfect graph if and only if for every induced subgraph H of G, H \in%DIFDELCMD < \varUpsilon%%% _k if and only if H \in%DIFDELCMD < \varOmega%%% _k for all k \in \mathbb{N .
Revised:  We find a nice characterization of this graph class in terms of \varOmega_k and \varUpsilon_k : We prove that a graph G is a neighborhood perfect graph if and only if for every induced subgraph H of G, H \in%DIFDELCMD < \varUpsilon%%% %DIFDELCMD < \varOmega%%% _k for all k \in \mathbb{N .
Edit intent: fluency
Original:  This document provides a brief introduction to Convolutional Neural Networks (CNNs) , discussing recently published papers and newly form techniques in developing these brilliantly fantastic image recognition models.
Revised:  This document provides a brief introduction to CNNs , discussing recently published papers and newly form techniques in developing these brilliantly fantastic image recognition models.
Edit intent: clarity
Original:  This document provides a brief introduction to Convolutional Neural Networks (CNNs) , discussing recently published papers and newly form techniques in developing these brilliantly fantastic image recognition models.
Revised:  This document provides a brief introduction to Convolutional Neural Networks (CNNs) , discussing recently published papers and newly formed techniques in developing these brilliantly fantastic image recognition models.
Edit intent: fluency
Original:  This introduction assumes you are familiar with the workings of neural networks and have some background in Artificial Intelligence .
Revised:  This introduction assumes you are familiar with the fundamentals of ANNs and machine learning .
Edit intent: clarity
Original: We study the surface fluctuations of a tissue with a dynamics dictated by cell-rearrangement, cell-division  and cell-death processes.
Revised: We study the surface fluctuations of a tissue with a dynamics dictated by cell-rearrangement, cell-division , and cell-death processes.
Edit intent: fluency
Original:  The obtained fluctuation spectrum can be mapped onto several other spectra such as those characterizing incompressible fluids, compressible Maxwell elastomers  or permeable membranes in appropriate asymptotic regimes.
Revised:  The obtained fluctuation spectrum can be mapped onto several other spectra such as those characterizing incompressible fluids, compressible Maxwell elastomers , or permeable membranes in appropriate asymptotic regimes.
Edit intent: fluency
Original: It was proposed earlier that Pfcrmp (Plasmodium falciparum chloroquine resistance marker protein) may be the chloroquine  target protein in nucleus.
Revised: It was proposed earlier that Pfcrmp (Plasmodium falciparum chloroquine resistance marker protein) may be the chloroquine 's target protein in nucleus.
Edit intent: clarity
Original:  In this communication, further evidence is presented to support the view that Pfcrmp may play akey role in chloroquine antimalarial actions as well as resistance development.
Revised:  In this communication, further evidence is presented to support the view that Pfcrmp may play a key role in chloroquine antimalarial actions as well as resistance development.
Edit intent: fluency
Original:  This result holds for two different notions of approximation by a polynomial: the standard definition of Nisan and Szegedy \mbox{ NS and the approximation by block-multilinear polynomials recently introduced by Aaronson and Ambainis (STOC'2015, arxiv:1411.5729).
Revised:  This result holds for two different notions of approximation by a polynomial: the standard definition of Nisan and Szegedy and the approximation by block-multilinear polynomials recently introduced by Aaronson and Ambainis (STOC'2015, arxiv:1411.5729).
Edit intent: coherence
Original:  In particular, we show that when G is a graph  of bounded expansion then \mathrm{xc _k(G))\leqslant \mathcal{O (f(k)\cdot n) for some function f . For general graphs we show that there is no function f such that, for all natural numbers k and for all graphs on n vertices, the extension complexity of \mathop{\mathrm{STAB _k(G) is at most f(k)\cdot n^{ \mathcal{O }.
Revised:  In particular, we show that when G is a graph of bounded expansion then \mathrm{xc _k(G))\leqslant O (f(k)\cdot n) for some function f . For general graphs we show that there is no function f such that, for all natural numbers k and for all graphs on n vertices, the extension complexity of \mathop{\mathrm{STAB _k(G) is at most f(k)\cdot n^{ \mathcal{O }.
Edit intent: fluency
Original:  In particular, we show that when G is a graph  of bounded expansion then \mathrm{xc _k(G))\leqslant \mathcal{O (f(k)\cdot n) for some function f . For general graphs we show that there is no function f such that, for all natural numbers k and for all graphs on n vertices, the extension complexity of \mathop{\mathrm{STAB _k(G) is at most f(k)\cdot n^{ \mathcal{O }.
Revised:  In particular, we show that when G is a graph of bounded expansion then \mathrm{xc _k(G))\leqslant \mathcal{O (f(k)\cdot n) for some function f . For general graphs we show that there is no function f such that, for all natural numbers k and for all graphs on n vertices, the extension complexity of \mathop{\mathrm{STAB _k(G) is at most f(k)\cdot n^{ \mathcal{O }.
Edit intent: fluency
Original:  In particular, we show that when G is a graph  of bounded expansion then \mathrm{xc _k(G))\leqslant \mathcal{O (f(k)\cdot n) for some function f . For general graphs we show that there is no function f such that, for all natural numbers k and for all graphs on n vertices, the extension complexity of \mathop{\mathrm{STAB _k(G) is at most f(k)\cdot n^{ \mathcal{O }.
Revised:  In particular, we show that when G is a graph of bounded expansion then \mathrm{xc _k(G))\leqslant \mathcal{O (f(k)\cdot n) for some function f . For general graphs we show that there is no function f such that, for all natural numbers k and for all graphs on n vertices, the extension complexity of STAB _k(G) is at most f(k)\cdot n^{ \mathcal{O }.
Edit intent: clarity
Original:  It is known that optimizing over STAB_k(G) is W 1%DIFDELCMD < ]%%% -hard and is FPT tractable for graphs of bounded expansion.
Revised:  1%DIFDELCMD < ]%%% -hard and is FPT tractable for graphs of bounded expansion.
Edit intent: coherence
Original:  We show analogous results for the extension complexity of STAB _k(G) . In particular, we show that when G is a graph from a class of bounded expansion then xc(STAB _k(G))\leqslant O (f(k)\cdot n) for some function f (depending only on the class ) . This result can be extended in a simple way to a wide range of similarly defined graph polytopes.
Revised:  We show analogous results for the extension complexity of STAB _k(G) . In particular, we show that when G is a graph from a class of bounded expansion it holds that xc(STAB _k(G))\leqslant O (f(k)\cdot n) for some function f (depending only on the class ) . This result can be extended in a simple way to a wide range of similarly defined graph polytopes.
Edit intent: clarity
Original:  We show analogous results for the extension complexity of STAB _k(G) . In particular, we show that when G is a graph from a class of bounded expansion then xc(STAB _k(G))\leqslant O (f(k)\cdot n) for some function f (depending only on the class ) . This result can be extended in a simple way to a wide range of similarly defined graph polytopes.
Revised:  We show analogous results for the extension complexity of STAB _k(G) . In particular, we show that when G is a graph from a class of bounded expansion then xc(STAB _k(G))\leqslant O (f(k)\cdot n) where the function f depends only on the class ) . This result can be extended in a simple way to a wide range of similarly defined graph polytopes.
Edit intent: clarity
Original:  We show analogous results for the extension complexity of STAB _k(G) . In particular, we show that when G is a graph from a class of bounded expansion then xc(STAB _k(G))\leqslant O (f(k)\cdot n) for some function f (depending only on the class ) . This result can be extended in a simple way to a wide range of similarly defined graph polytopes.
Revised:  We show analogous results for the extension complexity of STAB _k(G) . In particular, we show that when G is a graph from a class of bounded expansion then xc(STAB _k(G))\leqslant O (f(k)\cdot n) for some function f (depending only on the class . This result can be extended in a simple way to a wide range of similarly defined graph polytopes.
Edit intent: fluency
Original:  In case of general graphs we show that there is no function f {\em  such that, for all natural numbers k and for all graphs on n vertices, the extension complexity of STAB _k(G) is at most f(k)\cdot n^{ O(1) }  ] .
Revised:  In case of general graphs we show that there is f {\em such that, for all natural numbers k and for all graphs on n vertices, the extension complexity of STAB _k(G) is at most f(k)\cdot n^{ O(1) } ] .
Edit intent: clarity
Original:  In case of general graphs we show that there is no function f {\em  such that, for all natural numbers k and for all graphs on n vertices, the extension complexity of STAB _k(G) is at most f(k)\cdot n^{ O(1) }  ] .
Revised:  In case of general graphs we show that there is no function {\em such that, for all natural numbers k and for all graphs on n vertices, the extension complexity of STAB _k(G) is at most f(k)\cdot n^{ O(1) } ] .
Edit intent: fluency
Original:  We show a concrete model of UnCAL given by the lambdaG-calclus , which shows an interesting connection to lazy functional programming.
Revised:  We show a concrete model of UnCAL given by the lambdaG-calculus , which shows an interesting connection to lazy functional programming.
Edit intent: fluency
Original:  Finally, we obtain a linear lower bound on randomized one-sided error communication complexity of GHD^n_{0,\, t
Edit intent: coherence
Original:  We prove the existence of a cancellation time and a trading strategy for the seller which allow him/her to be super-hedged, whatever the model is .
Revised:  We study the existence of a cancellation time and a trading strategy for the seller which allow him/her to be super-hedged, whatever the model is .
Edit intent: clarity
Original:  We prove the existence of a cancellation time and a trading strategy for the seller which allow him/her to be super-hedged, whatever the model is .
Revised:  We prove the existence of a cancellation time and a trading strategy which allow the seller to be super-hedged, whatever the model is .
Edit intent: clarity
Original: Centrality measures are used to quantify the importance of a node in a given complex network.
Revised: Centrality measures have been defined to quantify the importance of a node in a given complex network.
Edit intent: clarity
Original:  In the present work, we calculate the degree centrality ranking of a node without having  entire network.
Revised:  In the present work, we predict the degree centrality ranking of a node without having entire network.
Edit intent: clarity
Original:  In the present work, we calculate the degree centrality ranking of a node without having  entire network.
Revised:  In the present work, we calculate the degree centrality rank of a node without having entire network.
Edit intent: fluency
Original:  In the present work, we calculate the degree centrality ranking of a node without having  entire network.
Revised:  In the present work, we calculate the degree centrality ranking of a node without having the entire network.
Edit intent: fluency
Original:  The proposed method uses degree centrality value of the node and few network parameters to calculate ranking of a node .
Revised:  The proposed method uses degree of the node and few network parameters to calculate ranking of a node .
Edit intent: clarity
Original:  The proposed method uses degree centrality value of the node and few network parameters to calculate ranking of a node .
Revised:  The proposed method uses degree centrality value of the node and some network parameters to calculate ranking of a node .
Edit intent: clarity
Original:  The proposed method uses degree centrality value of the node and few network parameters to calculate ranking of a node .
Revised:  The proposed method uses degree centrality value of the node and few network parameters to predict its rank .
Edit intent: clarity
Original:  These network parameters are total number of nodes , minimum, maximum  and average degree of the network.
Revised:  These network parameters are total number of nodes , minimum, maximum , and average degree of the network.
Edit intent: fluency
Original:  These parameters are calculated using sampling method .
Revised:  These parameters are estimated using random walk sampling techniques .
Edit intent: clarity
Original:  The proposed method is validated on Barabasi-Albert model . Simulation results show that the method gives good performance for higher degree nodes and it is decreased for lower degrees.
Revised:  The proposed method is validated on Barabasi-Albert networks . Simulation results show that the method gives good performance for higher degree nodes and it is decreased for lower degrees.
Edit intent: clarity
Original:  The proposed method is validated on Barabasi-Albert model . Simulation results show that the method gives good performance for higher degree nodes and it is decreased for lower degrees.
Revised:  The proposed method is validated on Barabasi-Albert model . Simulation results show that the proposed method predicts the rank of higher degree nodes and it is decreased for lower degrees.
Edit intent: clarity
Original:  To the best of our knowledge, ours is the first efficient deterministic protocol for this problem, if efficiency is measured in both the message size and the running time.
Revised:  To the best of our knowledge, ours is the first efficient deterministic protocol for this problem, if efficiency is measured in both the message size and the running time.
Edit intent: fluency