wanyu/IteraTeR_v2 huggingface dataset:
Original:  In a sizeable class of diffusion models, the large position limit is seen to arise naturally in conjunction with the limit of a complete model and hence approximations are most appropriate in this setting .
Revised:  In a sizeable class of diffusion models, the large position limit is seen to endogenously arise as the hedging error for the claim vanishes .
Edit intent: clarity
Original: Our main theoretical result is that, if a simple polytope has a pair of complementary vertices (i.e., two vertices with no facets in common), then it has a second such pair . Using this result, we improve adjacency testing for vertices in both simple and non-simple polytopes: given a polytope in the standard form {x \in Rn | Ax = b and x \geq 0} and a list of its V vertices, we describe an O(n) test to identify whether any two given vertices are adjacent.
Revised: Our main theoretical result is that, if a simple polytope has a pair of complementary vertices (i.e., two vertices with no facets in common), then it has a second such pair . Using this result, we improve adjacency testing for vertices in both simple and non-simple polytopes: given a polytope in the standard form {x \in R^n | Ax = b and x \geq 0} and a list of its V vertices, we describe an O(n) test to identify whether any two given vertices are adjacent.
Edit intent: clarity
Original:  We additionally present a somewhat more inclusive analysis, applicable for many early-career researchers, that is based on publications from 2006--2010 . Histograms and percentiles, plus top-performer lists, are presented for each category.
Revised:  We additionally present a somewhat more inclusive analysis, applicable for many early-career researchers, that is based on publications from 2006-2010 . Histograms and percentiles, plus top-performer lists, are presented for each category.
Edit intent: fluency
Original:  Finally, building on Hirsch's empirical equation, we find that the (10-year) h-index and  total citation count T can be approximated by the relation h = (0.5+ \sqrt{T  )/ \sqrt{5  for h > 5.
Revised:  Finally, building on Hirsch's empirical equation, we find that the (10-year) h-index and (10-year) total citation count T can be approximated by the relation h = (0.5+ \sqrt{T )/ \sqrt{5 for h > 5.
Edit intent: fluency
Original:  Finally, building on Hirsch's empirical equation, we find that the (10-year) h-index and  total citation count T can be approximated by the relation h = (0.5+ \sqrt{T  )/ \sqrt{5  for h > 5.
Revised:  Finally, building on Hirsch's empirical equation, we find that the (10-year) h-index and total citation count T can be approximated by the relation h = (0.5+ \sqrt{T T )/ \sqrt{5 for h > 5.
Edit intent: fluency
Original:  Finally, building on Hirsch's empirical equation, we find that the (10-year) h-index and  total citation count T can be approximated by the relation h = (0.5+ \sqrt{T  )/ \sqrt{5  for h > 5.
Revised:  Finally, building on Hirsch's empirical equation, we find that the (10-year) h-index and total citation count T can be approximated by the relation h = (0.5+ \sqrt{T )/ \sqrt{5 5 for h > 5.
Edit intent: fluency
Original: Over the years, we have been asked repeatedly whether we had ever implemented a certain polynomial method for deciding matrix total unimodularity.
Revised: This paper describes implementation and computational results of a polynomial test of total unimodularity.
Edit intent: clarity
Original:  This has been approximately done now, in an im- plementation of a simplified version of the test .
Revised:  The test is a simplified version of the test .
Edit intent: coherence
Original:  The program also tests for two related unimodularity properties.
Revised:  The program also decides two related unimodularity properties.
Edit intent: clarity
Original:  Our comparsion shows that the ruggedness of the empirical landscape is affected by whether the included mutations are beneficial or deleterious and by whether intra- or intergenic epistasis is involved.
Revised:  Our comparison shows that the ruggedness of the empirical landscape is affected by whether the included mutations are beneficial or deleterious and by whether intra- or intergenic epistasis is involved.
Edit intent: fluency
Original:  Finally, the empirical landscapes are compared to landscapes generated with the Rough Mt.  Fuji model.
Revised:  Finally, the empirical landscapes are compared to landscapes generated with the Rough Mt. \ Fuji model.
Edit intent: fluency
Original: Paths P_1 ,..., P_k in a graph G=(V,E) are said to be mutually induced if for any 1 <= i < j <= k, P_i and P_j have neither common vertices nor adjacent vertices (except perhaps their end-vertices).
Revised: Paths P1 ,..., P_k in a graph G=(V,E) are said to be mutually induced if for any 1 <= i < j <= k, P_i and P_j have neither common vertices nor adjacent vertices (except perhaps their end-vertices).
Edit intent: fluency
Original: Paths P_1 ,..., P_k in a graph G=(V,E) are said to be mutually induced if for any 1 <= i < j <= k, P_i and P_j have neither common vertices nor adjacent vertices (except perhaps their end-vertices).
Revised: Paths P_1 ,..., Pk in a graph G=(V,E) are said to be mutually induced if for any 1 <= i < j <= k, P_i and P_j have neither common vertices nor adjacent vertices (except perhaps their end-vertices).
Edit intent: fluency
Original:  The Induced Disjoint Paths problem is to test whether a graph G with k pairs of specified vertices ( s_i,t_i ) contains k mutually induced paths P_i such that P_i connects s_i and t_i for i=1,...,k.
Revised:  The Induced Disjoint Paths problem is to test whether a graph G with k pairs of specified vertices ( si,ti ) contains k mutually induced paths P_i such that P_i connects s_i and t_i for i=1,...,k.
Edit intent: clarity
Original:  Several related problems, such as the k-in-a-Path problem, are shown to be fixed-parameter tractable for claw-free graphs as well.
Revised:  Several related problems, such as the k-in-a-Path problem, are proven to be fixed-parameter tractable for claw-free graphs as well.
Edit intent: clarity
Original:  We also show that an improvement of these results in certain directions is unlikely, for example by observing that the Induced Disjoint Paths problem cannot have a polynomial kernel for line graphs (a type of claw-free graphs), unless NP \subseteq coNP/poly.
Revised:  We show that an improvement of these results in certain directions is unlikely, for example by observing that the Induced Disjoint Paths problem cannot have a polynomial kernel for line graphs (a type of claw-free graphs), unless NP \subseteq coNP/poly.
Edit intent: clarity
Original:  We also show that an improvement of these results in certain directions is unlikely, for example by observing that the Induced Disjoint Paths problem cannot have a polynomial kernel for line graphs (a type of claw-free graphs), unless NP \subseteq coNP/poly.
Revised:  We also show that an improvement of these results in certain directions is unlikely, for example by noting that the Induced Disjoint Paths problem cannot have a polynomial kernel for line graphs (a type of claw-free graphs), unless NP \subseteq coNP/poly.
Edit intent: clarity
Original: This paper investigates how a population of neuron-like agents can use metabolic cost to communicate the importance of their actions .
Revised: This paper investigates how neurons can use metabolic cost to communicate the importance of their actions .
Edit intent: clarity
Original:  Although decision-making by individual agents has been extensively studied, questions regarding how agents should behave to cooperate effectively remain largely unaddressed.
Revised:  Although decision-making by individual neurons has been extensively studied, questions regarding how agents should behave to cooperate effectively remain largely unaddressed.
Edit intent: style
Original:  Although decision-making by individual agents has been extensively studied, questions regarding how agents should behave to cooperate effectively remain largely unaddressed.
Revised:  Although decision-making by individual agents has been extensively studied, questions regarding how neurons should behave to cooperate effectively remain largely unaddressed.
Edit intent: style
Original: A  study on structural properties of regular and context-free languages has  promoted our basic understandings of the complex behaviors of those languages.
Revised: A recent study on structural properties of regular and context-free languages has promoted our basic understandings of the complex behaviors of those languages.
Edit intent: clarity
Original: A  study on structural properties of regular and context-free languages has  promoted our basic understandings of the complex behaviors of those languages.
Revised: A study on structural properties of regular and context-free languages has greatly promoted our basic understandings of the complex behaviors of those languages.
Edit intent: clarity
Original:  We continue the study to examine how regular languages behave when they are "almost halving" numerous infinite languages.
Revised:  We continue the study to examine how regular languages behave when they are asked to halve numerous infinite languages.
Edit intent: clarity
Original:  In particular , we are focused on a situation in which a regular language  " dissects " a target infinite language into two infinite subsets .
Revised:  A particular interest rests on a situation in which a regular language " dissects " a target infinite language into two infinite subsets .
Edit intent: clarity
Original:  In particular , we are focused on a situation in which a regular language  " dissects " a target infinite language into two infinite subsets .
Revised:  In particular , we are focused on a situation in which a regular language needs to " dissects " a target infinite language into two infinite subsets .
Edit intent: clarity
Original:  In particular , we are focused on a situation in which a regular language  " dissects " a target infinite language into two infinite subsets .
Revised:  In particular , we are focused on a situation in which a regular language " dissect " a target infinite language into two infinite subsets .
Edit intent: fluency
Original:  In particular , we are focused on a situation in which a regular language  " dissects " a target infinite language into two infinite subsets .
Revised:  In particular , we are focused on a situation in which a regular language " dissects " a given infinite language into two infinite subsets .
Edit intent: clarity
Original:  In particular , we are focused on a situation in which a regular language  " dissects " a target infinite language into two infinite subsets .
Revised:  In particular , we are focused on a situation in which a regular language " dissects " a target infinite language into two subsets of infinite sizes .
Edit intent: clarity
Original:  Every context-free language and its complement can be dissected by carefully chosen regular languages .
Revised:  Every context-free language is dissected by carefully chosen regular languages .
Edit intent: clarity
Original:  Under certain natural conditions, the complements and finite intersections of semi-linear languages become dissectable.
Revised:  Under certain natural conditions, complements and finite intersections of semi-linear languages become dissectable.
Edit intent: fluency
Original:  Similarly, restricted to bounded languages, the intersections of finitely many bounded context-free languages and, more surprisingly, the entire Boolean hierarchy over bounded context-free languages are dissectable .
Revised:  Similarly, restricted to bounded languages, the intersections of finitely many context-free languages and, more surprisingly, the entire Boolean hierarchy over bounded context-free languages are dissectable .
Edit intent: fluency
Original:  Similarly, restricted to bounded languages, the intersections of finitely many bounded context-free languages and, more surprisingly, the entire Boolean hierarchy over bounded context-free languages are dissectable .
Revised:  Similarly, restricted to bounded languages, the intersections of finitely many bounded context-free languages and, more surprisingly, the entire Boolean hierarchy over bounded context-free languages are REG-dissectible .
Edit intent: clarity
Original:  As an immediate application  , we show a structural property in which an appropriate bounded context-free language can separate, with infinite margins , two given infinite bounded context-free languages , one of which contains the other with an infinite margin.
Revised:  As an immediate application , we show another structural property, in which an appropriate bounded context-free language can separate, with infinite margins , two given infinite bounded context-free languages , one of which contains the other with an infinite margin.
Edit intent: clarity
Original:  As an immediate application  , we show a structural property in which an appropriate bounded context-free language can separate, with infinite margins , two given infinite bounded context-free languages , one of which contains the other with an infinite margin.
Revised:  As an immediate application , we show a structural property in which an appropriate bounded context-free language can "separate with infinite margins , two given infinite bounded context-free languages , one of which contains the other with an infinite margin.
Edit intent: clarity
Original:  We continue the study to examine how regular languages behave when they are asked to halve numerous infinite languages.
Revised:  We continue the study to examine how regular languages behave when they need to cut numerous infinite languages.
Edit intent: clarity
Original:  A particular interest rests on a situation in which a regular language needs to "dissect" a given infinite language into two subsets of infinite sizes .
Revised:  A particular interest rests on a situation in which a regular language needs to "dissect" a given infinite language into two subsets of infinite size .
Edit intent: fluency
Original: Decision making of agents who are members of a society is analyzed from the point of view of quantum decision theory.
Revised: Decision making of agents , who are interacting members of a society is analyzed from the point of view of quantum decision theory.
Edit intent: clarity
Original:  This generalizes the approach, developed earlier by the authors for separate individuals , to decision making under the influence of social interactions .
Revised:  This generalizes the approach, developed earlier by the authors for separate individuals .
Edit intent: clarity
Original:  The discrete models leads itself naturally to numerical implementation.
Revised:  The discrete models lends itself naturally to numerical implementation.
Edit intent: fluency
Original:  We then present a system of signal passing tiles that simulate an arbitrary Turing machine which is fuel efficient in that only a constant number of tiles are used up per computation step.
Revised:  We then present a system of signal passing tiles that simulate an arbitrary Turing machine which is fuel efficient in that only a constant number of tiles are used up per computation step.
Edit intent: fluency
Original: In this paper we study the power of a model of tile self-assembly in which individual tiles of the system have the ability to turn on or off glue types based on the bonding of other glues on the given tile.
Revised: In this paper we demonstrate the power of a model of tile self-assembly in which individual tiles of the system have the ability to turn on or off glue types based on the bonding of other glues on the given tile.
Edit intent: clarity
Original:  We formulate the Signal passing Tile Assembly Model which is based on the model of Padilla, et al. (2012), but is asynchronousin that any action of turning a glue on or off, or attaching a new tile, or the breaking apart of an assembly , may happen in any order.
Revised:  We formulate the Signal-passing Tile Assembly Model which is based on the model of Padilla, et al. (2012), but is asynchronousin that any action of turning a glue on or off, or attaching a new tile, or the breaking apart of an assembly , may happen in any order.
Edit intent: fluency
Original:  We formulate the Signal passing Tile Assembly Model which is based on the model of Padilla, et al. (2012), but is asynchronousin that any action of turning a glue on or off, or attaching a new tile, or the breaking apart of an assembly , may happen in any order.
Revised:  We formulate the Signal passing Tile Assembly Model (STAM), based on the model of Padilla, et al. (2012), but is asynchronousin that any action of turning a glue on or off, or attaching a new tile, or the breaking apart of an assembly , may happen in any order.
Edit intent: clarity
Original:  We formulate the Signal passing Tile Assembly Model which is based on the model of Padilla, et al. (2012), but is asynchronousin that any action of turning a glue on or off, or attaching a new tile, or the breaking apart of an assembly , may happen in any order.
Revised:  We formulate the Signal passing Tile Assembly Model which is based on the model of Padilla, et al. (2012), but is asynchronousin that any action of turning a glue on or off, attaching a new tile, or the breaking apart of an assembly , may happen in any order.
Edit intent: fluency
Original:  We formulate the Signal passing Tile Assembly Model which is based on the model of Padilla, et al. (2012), but is asynchronousin that any action of turning a glue on or off, or attaching a new tile, or the breaking apart of an assembly , may happen in any order.
Revised:  We formulate the Signal passing Tile Assembly Model which is based on the model of Padilla, et al. (2012), but is asynchronousin that any action of turning a glue on or off, or attaching a new tile, or breaking apart an assembly to happen in any order.
Edit intent: clarity
Original:  Within this most general case we study tile self-assembly problems that have been addressed within the abstract Tile Assembly Model , as well as other variantsof that model, and show that signal passing tiles allow for substantial improvement across multiple  metrics.
Revised:  Within this most general case we study tile self-assembly problems that have been addressed within the abstract Tile Assembly Model and its variants, showing that signal passing tiles allow for substantial improvement across multiple metrics.
Edit intent: clarity
Original:  Our first results focus on the tile type efficient assembly of linear structures, which achieves assembly using provably fewer tile types than what is possible in standard tile assembly models by utilizing a recursive assembly process.
Revised:  Our first result utilizes a recursive assembly process to achieve tile-type efficient assembly of linear structures, which achieves assembly using provably fewer tile types than what is possible in standard tile assembly models by utilizing a recursive assembly process.
Edit intent: clarity
Original:  Our first results focus on the tile type efficient assembly of linear structures, which achieves assembly using provably fewer tile types than what is possible in standard tile assembly models by utilizing a recursive assembly process.
Revised:  Our first results focus on the tile type efficient assembly of linear structures, using provably fewer tile types than what is possible in standard tile assembly models by utilizing a recursive assembly process.
Edit intent: coherence
Original:  We then present a system of signal passing tiles that simulate an arbitrary Turing machine which is fuel efficient in that only a constant number of tiles are used up per computation step.
Revised:  We then present a system of signal passing tiles that simulate an arbitrary Turing machine which is fuel efficient in that only a constant number of tiles per computation step.
Edit intent: clarity
Original:  Finally, we consider the assembly of the discrete Sierpinski triangle and show that this pattern can be strictly self-assembled within the signal tile passing model .
Revised:  Finally, we consider the assembly of the discrete Sierpinski triangle , demonstrating that this pattern can be strictly self-assembled within the signal tile passing model .
Edit intent: clarity
Original:  Finally, we consider the assembly of the discrete Sierpinski triangle and show that this pattern can be strictly self-assembled within the signal tile passing model .
Revised:  Finally, we consider the assembly of the discrete Sierpinski triangle and show that this pattern can be strictly self-assembled within the STAM .
Edit intent: clarity
Original:  Moreover, we show that the same short path exists in%DIFDELCMD < \Y4 %%% graphs, a subgraph of L_\infty-Delaunay triangulations, and therefore we determine the stretch factor for these graphs too.
Revised:  %DIFDELCMD < \Y4 %%% graphs, a subgraph of L_\infty-Delaunay triangulations, and therefore we determine the stretch factor for these graphs too.
Edit intent: coherence
Original:  Moreover, we show that the same short path exists in%DIFDELCMD < \Y4 %%% graphs, a subgraph of L_\infty-Delaunay triangulations, and therefore we determine the stretch factor for these graphs too.
Revised:  Moreover, we show that the same short path exists in%DIFDELCMD < \Y4 %%% 
Edit intent: coherence
Original: We present a new framework for studying C \infty\C -words, that are arbitrarily many times differentiable words over the alphabet \Sigma%DIFDELCMD < } %%% = 1,2%DIFDELCMD < }%%% . After introducing an equivalence relation on C \infty\C -words , whose classes are called minimal classes and represent all the C \infty%DIFDELCMD < }%%% -words, we define a vertical coding of these words based on a three-letter alphabet, and a set of functions operating over this representation.
Revised: We present a new framework for \infty\C -words, that are arbitrarily many times differentiable words over the alphabet \Sigma%DIFDELCMD < } %%% = 1,2%DIFDELCMD < }%%% . After introducing an equivalence relation on C \infty\C -words , whose classes are called minimal classes and represent all the C \infty%DIFDELCMD < }%%% -words, we define a vertical coding of these words based on a three-letter alphabet, and a set of functions operating over this representation.
Edit intent: clarity
Original: We present a new framework for studying C \infty\C -words, that are arbitrarily many times differentiable words over the alphabet \Sigma%DIFDELCMD < } %%% = 1,2%DIFDELCMD < }%%% . After introducing an equivalence relation on C \infty\C -words , whose classes are called minimal classes and represent all the C \infty%DIFDELCMD < }%%% -words, we define a vertical coding of these words based on a three-letter alphabet, and a set of functions operating over this representation.
Revised: We present a new framework for studying C dealing with\C -words, that are arbitrarily many times differentiable words over the alphabet \Sigma%DIFDELCMD < } %%% = 1,2%DIFDELCMD < }%%% . After introducing an equivalence relation on C \infty\C -words , whose classes are called minimal classes and represent all the C \infty%DIFDELCMD < }%%% -words, we define a vertical coding of these words based on a three-letter alphabet, and a set of functions operating over this representation.
Edit intent: clarity
Original: We present a new framework for studying C \infty\C -words, that are arbitrarily many times differentiable words over the alphabet \Sigma%DIFDELCMD < } %%% = 1,2%DIFDELCMD < }%%% . After introducing an equivalence relation on C \infty\C -words , whose classes are called minimal classes and represent all the C \infty%DIFDELCMD < }%%% -words, we define a vertical coding of these words based on a three-letter alphabet, and a set of functions operating over this representation.
Revised: We present a new framework for studying C \infty\C -words, \Sigma%DIFDELCMD < } %%% = 1,2%DIFDELCMD < }%%% . After introducing an equivalence relation on C \infty\C -words , whose classes are called minimal classes and represent all the C \infty%DIFDELCMD < }%%% -words, we define a vertical coding of these words based on a three-letter alphabet, and a set of functions operating over this representation.
Edit intent: coherence