wanyu/IteraTeR_v2 huggingface dataset:
Original:  Furthermore, we investigate the relationship between the dual diameter and the number of ears (triangles with exactly two edges incident to the boundary of \mathcal{P \Poly ) in a triangulation.
Revised:  Furthermore, we investigate the relationship between the dual diameter and the number of ears (triangles with exactly two edges incident to the boundary of \Poly ) in a triangulation.
Edit intent: clarity
Original: Motivated by applications in telecommunications, computer science and physics, we consider a discrete-time Markov process with restart in the Borel state space .
Revised: Motivated by applications in telecommunications, computer scienceand physics, we consider a discrete-time Markov process with restart in the Borel state space .
Edit intent: fluency
Original: Motivated by applications in telecommunications, computer science and physics, we consider a discrete-time Markov process with restart in the Borel state space .
Revised: Motivated by applications in telecommunications, computer science and physics, we consider a discrete-time Markov process withrestart .
Edit intent: clarity
Original:  At each step the process either with a positive probability restarts from a given distribution, or with the complementary probability continues according to a Markov transition kernel.
Revised:  At each step the process eitherwith a positive probability restarts from a given distribution, or with the complementary probability continues according to a Markov transition kernel.
Edit intent: fluency
Original:  At each step the process either with a positive probability restarts from a given distribution, or with the complementary probability continues according to a Markov transition kernel.
Revised:  At each step the process either with a positive probability restarts from a given distribution, orwith the complementary probability continues according to a Markov transition kernel.
Edit intent: fluency
Original:  At each step the process either with a positive probability restarts from a given distribution, or with the complementary probability continues according to a Markov transition kernel.
Revised:  At each step the process either with a positive probability restarts from a given distribution, or with the complementary probability continues according to a Markovtransition kernel.
Edit intent: fluency
Original:  The main focus of the present work is  the expectation of the hitting time (to a given target set) of the process with restart , for which we obtain the explicit formula.
Revised:  The main contribution of the present work is the expectation of the hitting time (to a given target set) of the process with restart , for which we obtain the explicit formula.
Edit intent: clarity
Original:  The main focus of the present work is  the expectation of the hitting time (to a given target set) of the process with restart , for which we obtain the explicit formula.
Revised:  The main focus of the present work is thatwe obtain an explicit expression for the expectation of the hitting time (to a given target set) of the process with restart , for which we obtain the explicit formula.
Edit intent: clarity
Original:  The main focus of the present work is  the expectation of the hitting time (to a given target set) of the process with restart , for which we obtain the explicit formula.
Revised:  The main focus of the present work is the expectation of the hittingtime (to a given target set) of the process with restart , for which we obtain the explicit formula.
Edit intent: fluency
Original: We illustrate our results with two examples in uncountable and countable state spaces  .
Revised: We illustrate our results with two examplesin uncountable and countable state spaces .
Edit intent: fluency
Original:   We show that sensible cross-language design decisions can be made in the face of different semantics, and that composed programs have an acceptable performance overhead of, at most, just over 2x.
Revised:  We show that good solutions can be found to the design challenges; and that the resulting implementation imposes an acceptable performance overhead of, at most, just over 2x.
Edit intent: clarity
Original:  We received about 1,100 applications and each applicant had the opportunity to list up to five %DIFDELCMD < {\em %DIFDELCMD < %%% influential works in the general field of "Big Data" for scientific discovery.
Revised:  We received about 1,100 applications and each applicant had the opportunity to list up to five %DIFDELCMD < {\em %DIFDELCMD < %%% influential works in the general field of "Big Data" for scientific discovery.
Edit intent: fluency
Original:  We show that Clarkson's sampling algorithm can be applied to two separate problems in computational algebra: solving large-scale polynomial systems, for which we utilize a Helly-type result for algebraic varieties, and finding small generating sets of graded ideals.
Revised:  We show that Clarkson's sampling algorithm can be applied to two problems in computational algebra: solving large-scale polynomial systems, for which we utilize a Helly-type result for algebraic varieties, and finding small generating sets of graded ideals.
Edit intent: clarity
Original: This paper transfers a randomized algorithm  originally used in geometric optimization to computational commutative algebra.
Revised: This paper transfers a randomized algorithm , originally used in geometric optimization to computational commutative algebra.
Edit intent: fluency
Original: This paper transfers a randomized algorithm  originally used in geometric optimization to computational commutative algebra.
Revised: This paper transfers a randomized algorithm originally used in geometric optimization , to computational problems in commutative algebra.
Edit intent: clarity
Original:  We show that Clarkson's sampling algorithm can be applied to two problems in computational algebra: solving large-scale polynomial systems , for which we utilize a Helly-type result for algebraic varieties, and finding small generating sets of graded ideals.
Revised:  We show that Clarkson's sampling algorithm can be applied to two problems in computational algebra: solving large-scale polynomial systems and finding small generating sets of graded ideals.
Edit intent: coherence
Original:  The cornerstone of our work is showing that the theory of violator spaces of G\"artner et al.\ applies to these polynomial ideal problems.
Revised:  The cornerstone of our work is showing that the theory of violator spaces of G\"artner et al.\ applies to polynomial ideal problems.
Edit intent: clarity
Original:   The resulting algorithms have expected runtime linear in the number of input polynomials, making the method particularly interesting for handling systems with very large numbers of polynomials, but whose rank in the vector space of polynomials is small (e.g., when the number of variables  is constant).
Revised:  The resulting algorithms have expected runtime linear in the number of input polynomials, making the ideas interesting for handling systems with very large numbers of polynomials, but whose rank in the vector space of polynomials is small (e.g., when the number of variables is constant).
Edit intent: clarity
Original:  "Modal" is used by the Planck satellite experiment for constraining general non-Gaussian models of the early universe via the bispectrum  of the cosmic microwave background  .
Revised:  "Modal" is used by the Planck satellite experiment for constraining general non-Gaussian models of the early universe via the bispectrum of the cosmic microwave background radiation .
Edit intent: clarity
Original:  We focus on the hot-spot of the code which is the projection of bispectra from the end of inflation to  spherical shell at decoupling  which defines the CMB we observe  .
Revised:  We focus on one particular element of the code which is the projection of bispectra from the end of inflation to spherical shell at decoupling which defines the CMB we observe .
Edit intent: clarity
Original:  We focus on the hot-spot of the code which is the projection of bispectra from the end of inflation to  spherical shell at decoupling  which defines the CMB we observe  .
Revised:  We focus on the hot-spot of the code : the projection of bispectra from the end of inflation to spherical shell at decoupling which defines the CMB we observe .
Edit intent: coherence
Original:  We focus on the hot-spot of the code which is the projection of bispectra from the end of inflation to  spherical shell at decoupling  which defines the CMB we observe  .
Revised:  We focus on the hot-spot of the code which is the projection of bispectra from the end of inflation to the spherical shell at decoupling which defines the CMB we observe .
Edit intent: fluency
Original:  We focus on the hot-spot of the code which is the projection of bispectra from the end of inflation to  spherical shell at decoupling  which defines the CMB we observe  .
Revised:  We focus on the hot-spot of the code which is the projection of bispectra from the end of inflation to spherical shell at decoupling , which defines the CMB we observe .
Edit intent: fluency
Original:  We show that by employing separable methods this calculation can be reduced to a one dimensional summation plus two integrations reducing the dimensionality from four to three.
Revised:  We show that by employing separable methods this calculation can be reduced to a one-dimensional summation plus two integrations reducing the dimensionality from four to three.
Edit intent: fluency
Original:  We show that by employing separable methods this calculation can be reduced to a one dimensional summation plus two integrations reducing the dimensionality from four to three.
Revised:  We show that by employing separable methods this calculation can be reduced to a one dimensional summation plus two integrations , reducing the overall dimensionality from four to three.
Edit intent: clarity
Original:  We demonstrate speed-ups of over 100x, arising from a combination of algorithmic improvements and architecture-aware optimizations targeted at improving thread and vectorization behaviour.
Revised:  We demonstrate speed-ups of ~ 100x, arising from a combination of algorithmic improvements and architecture-aware optimizations targeted at improving thread and vectorization behaviour.
Edit intent: clarity
Original:  We demonstrate speed-ups of over 100x, arising from a combination of algorithmic improvements and architecture-aware optimizations targeted at improving thread and vectorization behaviour.
Revised:  We demonstrate speed-ups of over 100x, arising from a combination of algorithmic improvements and architecture-aware optimisations targeted at improving thread and vectorization behaviour.
Edit intent: fluency
Original:  We demonstrate speed-ups of over 100x, arising from a combination of algorithmic improvements and architecture-aware optimizations targeted at improving thread and vectorization behaviour.
Revised:  We demonstrate speed-ups of over 100x, arising from a combination of algorithmic improvements and architecture-aware optimizations targeted at improving thread and vectorisation behaviour.
Edit intent: fluency
Original:  Our contributions to address this problem are: uniform treatment of small and big objects through the idea of virtual spans, efficiently and effectively reclaiming unused memory through fast and scalable global data structures, and constant-time (modulo synchronization) allocation and deallocation operations that trade off memory reuse and spatial locality without being subject to false sharing .
Revised:  Our contributions to address this problem are: uniform treatment of small and big objects through so-called virtual spans, efficiently and effectively reclaiming unused memory through fast and scalable global data structures, and constant-time (modulo synchronization) allocation and deallocation operations that trade off memory reuse and spatial locality without being subject to false sharing .
Edit intent: clarity
Original:  Our contributions to address this problem are: uniform treatment of small and big objects through the idea of virtual spans, efficiently and effectively reclaiming unused memory through fast and scalable global data structures, and constant-time (modulo synchronization) allocation and deallocation operations that trade off memory reuse and spatial locality without being subject to false sharing .
Revised:  Our contributions to address this problem are: uniform treatment of small and big objects through the idea of virtual spans, efficiently and effectively reclaiming free memory through fast and scalable global data structures, and constant-time (modulo synchronization) allocation and deallocation operations that trade off memory reuse and spatial locality without being subject to false sharing .
Edit intent: clarity
Original:   Using tools from memoryless computation, it is established that there is no universal transformation of size n that may simulate every transformation of A^n , but there is such a universal transformation when the size is n+2.
Revised:  Using tools from memoryless computation, it is established that there is no universal transformation of size n , but there is such a universal transformation when the size is n+2.
Edit intent: clarity
Original:   Using tools from memoryless computation, it is established that there is no universal transformation of size n that may simulate every transformation of A^n , but there is such a universal transformation when the size is n+2.
Revised:  Using tools from memoryless computation, it is established that there is no universal transformation of size n that may simulate every transformation of A^n , but there is such a transformation of size n+2.
Edit intent: coherence
Original:   minimal examples and bounds for the size and time of simulation in this case are determined.
Revised:  in this case, minimal examples and bounds for the size and time of simulation in this case are determined.
Edit intent: coherence
Original:   minimal examples and bounds for the size and time of simulation in this case are determined.
Revised:  minimal examples and bounds for the size and time of simulation are determined.
Edit intent: clarity
Original:  This illustrates the strengths and weaknesses of parallel models of computations , such as cellular automata.
Revised:  This illustrates the strengths and weaknesses of parallel models of computation , such as cellular automata.
Edit intent: fluency
Original: Let A be a finite set and n \geq 2.
Revised: Consider a finite set and n \geq 2.
Edit intent: clarity
Original:  For m \geq n, a transformation of A^m is defined as n-universal of size m if it may simulate every transformation of A^n by updating one coordinate (or register) at a time.
Revised:  For m \geq n, a transformation of A^m is n-complete of size m if it may simulate every transformation of A^n by updating one coordinate (or register) at a time.
Edit intent: clarity
Original:  Using tools from memoryless computation, it is established that there is no n-universal transformation of size n, but there is such a transformation of size n+ 2. An n-universal transformation is defined as complete if it may sequentially simulate every finite sequence of transformations of A^n;
Revised:  Using tools from memoryless computation, it is established that there is no n-complete transformation of size n, but there is such a transformation of size n+ 2. An n-universal transformation is defined as complete if it may sequentially simulate every finite sequence of transformations of A^n;
Edit intent: clarity
Original:  It is also shown that there is no n-universal transformation that updates all the registers in parallel, but that there exists a complete one that updates all but one register in parallel.
Revised:  It is also shown that there is no n-complete transformation that updates all the registers in parallel, but that there exists a complete one that updates all but one register in parallel.
Edit intent: clarity
Original:  So far, however, the notion of centrality in TVG scenarios usually refers to metrics that assess the relative importance of nodes along the temporal evolution of the network.
Revised:  Nevertheless, so far, the notion of centrality in TVG scenarios usually refers to metrics that assess the relative importance of nodes along the temporal evolution of the network.
Edit intent: coherence
Original:  Nevertheless, for some TVG scenarios,  more important than identifying the central nodes under a given  definition is identifying the key time instants for taking certain actions.
Revised:  Nevertheless, for some TVG scenarios, however, more important than identifying the central nodes under a given definition is identifying the key time instants for taking certain actions.
Edit intent: coherence
Original:  Nevertheless, for some TVG scenarios,  more important than identifying the central nodes under a given  definition is identifying the key time instants for taking certain actions.
Revised:  Nevertheless, for some TVG scenarios, more important than identifying the central nodes under a given definition is identifying the key time instants for taking certain actions.
Edit intent: fluency
Original:  In this paper, we introduce the notion of time centrality in TVGs.
Revised:  In this paper, we thus introduce and investigate the notion of time centrality in TVGs.
Edit intent: clarity
Original:  In this paper, we introduce the notion of time centrality in TVGs.
Revised:  In this paper, we introduce the notion of time centrality in TVGs.
Edit intent: fluency
Original:  We present two time centrality metrics related to diffusion processes.
Revised:  In this context, we present two time centrality metrics related to diffusion processes.
Edit intent: clarity
Original:  We evaluate the two defined metrics using a real-world dataset representing a in-person contact dynamic network.
Revised:  We evaluate the two defined metrics using a real-world dataset representing an in-person contact dynamic network.
Edit intent: fluency
Original:  We evaluate the two defined metrics using  a real-world dataset representing an in-person contact dynamic network  .
Revised:  We evaluate the two defined metrics using both a real-world dataset representing an in-person contact dynamic network .
Edit intent: clarity
Original:  Their low-complexity decoding algorithms render them attractive for use in software-defined radio applications where computational resources are limited.
Revised:  Their low-complexity decoding algorithms rendering them attractive for use in software-defined radio applications where computational resources are limited.
Edit intent: fluency
Original:  Finally, we show that the energy efficiency of the proposed decoders , running on desktop a processor, is comparable to state of the art software polar decoders.
Revised:  Finally, we show that the energy efficiency of the proposed decoders is comparable to state of the art software polar decoders.
Edit intent: clarity
Original:  Finally, we show that the energy efficiency of the proposed decoders , running on desktop a processor, is comparable to state of the art software polar decoders.
Revised:  Finally, we show that the energy efficiency of the proposed decoders , running on desktop a processor, is comparable to state-of-the-art software polar decoders.
Edit intent: fluency
Original:  Accurate estimates of CHA are critical for understanding of hydration effects ubiquitous in chemistry and biology.
Revised:  Accurate estimates of CHA are critical for understanding hydration effects ubiquitous in chemistry and biology.
Edit intent: fluency
Original:  Specifically, from a set of 504 small molecules we identify two pairs that are analogous, with respect to CHA, to the K+/F- pair -- a classical probe for the effect.
Revised:  Specifically, from a set of 504 small molecules we identify two pairs that are analogous, with respect to CHA, to the K+/F- pair--a classical probe for the effect.
Edit intent: fluency
Original:  The ability of widely used classical water models to predict hydration energies of small molecules strongly correlates with their ability to predict CHA.
Revised:  The ability of widely used classical water models to predict hydration energies of small molecules correlates with their ability to predict CHA.
Edit intent: clarity
Original:  On the other hand, the author shows that the gap problem of this type of weighted k-CSP can be solved by Hast's Algorithm BiLin in polynomial time, when k is sufficiently large, the support of its predicate is combined by the grounds of three truncated biased pairwise independent distributions that can be disguised to a balanced pairwise independent distribution and the three biases satisfy certain conditions .
Revised:  On the other hand, the author shows that the gap problem of this type of weighted k-CSP can be solved by Hast's Algorithm BiLin in polynomial time, when k is sufficiently large, the support of its predicate is combined by the grounds of three truncated biased pairwise independent distributions that can be disguised to a balanced pairwise independent distribution .
Edit intent: coherence
Original: of its predicate the ground of a balanced pairwise independent distribution is approximation resistant under weak form of d-to-1 Conjecture for any constant d%DIFDELCMD < \ge %%% 1. The main ingredients of the paper include a key issue in dictatorship test that generates the questions of the verifier as a balanced pairwise independent distribution and an invariance-style theorem that eliminates correlation of answers of all players to prove hardness from d-blocked k-Label-Cover,
Revised: of its predicate the ground of a %DIFDELCMD < \ge %%% 1. The main ingredients of the paper include a key issue in dictatorship test that generates the questions of the verifier as a balanced pairwise independent distribution and an invariance-style theorem that eliminates correlation of answers of all players to prove hardness from d-blocked k-Label-Cover,
Edit intent: clarity
Original:  On the other hand, the author shows that the gap problem of this type of weighted k-CSP can be solved by Hast's Algorithm BiLin in polynomial time, when k is sufficiently large, the support of its predicate is combined by the grounds of three uniformly negatively correlated distributions with certain biases that can be disguised to a balanced pairwise independent distribution .
Revised:  On the other hand, the author shows that the gap problem of this type of weighted k-CSP can be solved by Hast's Algorithm in polynomial time, when k is sufficiently large, the support of its predicate is combined by the grounds of three uniformly negatively correlated distributions with certain biases that can be disguised to a balanced pairwise independent distribution .
Edit intent: clarity
Original:  On the other hand, the author shows that the gap problem of this type of weighted k-CSP can be solved by Hast's Algorithm BiLin in polynomial time, when k is sufficiently large, the support of its predicate is combined by the grounds of three uniformly negatively correlated distributions with certain biases that can be disguised to a balanced pairwise independent distribution .
Revised:  On the other hand, the author shows that the gap problem of this type of weighted k-CSP can be solved by Hast's Algorithm BiLin in polynomial time, when k is sufficiently large, the support of its predicate is combined by the grounds of three truncated biased pairwise independent distributions and the three biases satisfy certain conditions .
Edit intent: clarity
Original:  To conclude, the author refutes Unique Game Conjecture and d-to-1 Conjecture for any constant d%DIFDELCMD < \ge %%% 2 , assuming P\ne NP.
Revised:  To conclude, the author refutes Unique Game Conjecture %DIFDELCMD < \ge %%% 2 , assuming P\ne NP.
Edit intent: clarity