wanyu/IteraTeR_v2 huggingface dataset:
Original:  The authors prove Unique Game Conjecture holds true on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1) , and Unique Game Conjecture holds true on GUGP-PWT(1/2)  if the 2-to-1 Conjecture holds true.
Revised:  The authors prove Unique Game Conjecture on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1) , and Unique Game Conjecture holds true on GUGP-PWT(1/2) if the 2-to-1 Conjecture holds true.
Edit intent: fluency
Original:  The authors prove Unique Game Conjecture holds true on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1) , and Unique Game Conjecture holds true on GUGP-PWT(1/2)  if the 2-to-1 Conjecture holds true.
Revised:  The authors prove Unique Game Conjecture holds true on GUGP-PWT(1) holds true , and Unique Game Conjecture holds true on GUGP-PWT(1/2) if the 2-to-1 Conjecture holds true.
Edit intent: coherence
Original:  The authors prove Unique Game Conjecture holds true on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1) , and Unique Game Conjecture holds true on GUGP-PWT(1/2)  if the 2-to-1 Conjecture holds true.
Revised:  The authors prove Unique Game Conjecture holds true on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1) , and Unique Game Conjecture on GUGP-PWT(1/2) if the 2-to-1 Conjecture holds true.
Edit intent: fluency
Original:  The authors prove Unique Game Conjecture holds true on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1) , and Unique Game Conjecture holds true on GUGP-PWT(1/2)  if the 2-to-1 Conjecture holds true.
Revised:  The authors prove Unique Game Conjecture holds true on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1) , and Unique Game Conjecture holds true on GUGP-PWT(1/2) holds true, if the 2-to-1 Conjecture holds true.
Edit intent: fluency
Original:  The authors pose an open problem whether Unique Game Conjecture holds true on GUGP-PWT(\rho) with 0<\rho<1.
Revised:  The author poses an open problem whether Unique Game Conjecture holds true on GUGP-PWT(\rho) with 0<\rho<1.
Edit intent: fluency
Original:  We also discuss the question of cardinality of the used alphabet, and we are able to modify our algorithm in order to work in a smaller alphabet.
Revised:  We also discuss the question of cardinality of the used alphabet, and we are able to modify our algorithm in order to work with a smaller alphabet.
Edit intent: fluency
Original:  This alphabet cannot be diminished any more.
Revised:  This alphabet cannot be reduced any more.
Edit intent: clarity
Original:  First, we derive partial and full link reversal algorithms that are oblivious to one-hop neighbor information, and convert a destination-disoriented DAG to a destination-oriented DAG.
Revised:  First, we derive partial and full link reversal algorithms that do not require one-hop neighbor information, and convert a destination-disoriented DAG to a destination-oriented DAG.
Edit intent: clarity
Original:  We embed these  in the framework of Gafni and Bertsekas ("Distributed algorithms for generating loop-free routes in networks with frequently changing topology", 1981) in order to establish their termination properties.
Revised:  We embed these algorithms in the framework of Gafni and Bertsekas ("Distributed algorithms for generating loop-free routes in networks with frequently changing topology", 1981) in order to establish their termination properties.
Edit intent: fluency
Original: In a convex n-gon, let d _1 > d _2 > ... denote the set of all distances between pairs of vertices, and let m _i be the number of pairs of vertices at distance d _i from one another.
Revised: In a convex n-gon, let d 1 > d _2 > ... denote the set of all distances between pairs of vertices, and let m _i be the number of pairs of vertices at distance d _i from one another.
Edit intent: fluency
Original: In a convex n-gon, let d _1 > d _2 > ... denote the set of all distances between pairs of vertices, and let m _i be the number of pairs of vertices at distance d _i from one another.
Revised: In a convex n-gon, let d _1 > d 2 > ... denote the set of all distances between pairs of vertices, and let m _i be the number of pairs of vertices at distance d _i from one another.
Edit intent: fluency
Original: In a convex n-gon, let d _1 > d _2 > ... denote the set of all distances between pairs of vertices, and let m _i be the number of pairs of vertices at distance d _i from one another.
Revised: In a convex n-gon, let d _1 > d _2 > ... denote the set of all distances between pairs of vertices, and let m i be the number of pairs of vertices at distance d _i from one another.
Edit intent: fluency
Original: In a convex n-gon, let d _1 > d _2 > ... denote the set of all distances between pairs of vertices, and let m _i be the number of pairs of vertices at distance d _i from one another.
Revised: In a convex n-gon, let d _1 > d _2 > ... denote the set of all distances between pairs of vertices, and let m _i be the number of pairs of vertices at distance d i from one another.
Edit intent: fluency
Original:  We prove that m_1  + ... + m _k <= (2k-1)n, making progress towards the conjecture m_1 + . .. + m_k of Erdos, Lovasz, and Vesztergombi.
Revised:  We prove that m_1 + ... + m k <= (2k-1)n, making progress towards the conjecture m_1 + . .. + m_k of Erdos, Lovasz, and Vesztergombi.
Edit intent: fluency
Original:  Yet latency-sensitive applications still frequently build on in-order TCP despite its performance drawbacks, for reasons such as network compatibility and TCP's cultural inertia.
Revised:  Yet latency-sensitive applications still frequently build on in-order semantics from a convenience blessing to a performance curse. As Internet evolution makes TCP's cultural inertia.
Edit intent: clarity
Original:  Experiments suggest that Minion can noticeably improve the performance of applications such as conferencing, virtual private networking, and web browsing, while incurring minimal CPU or bandwidth costs.
Revised:  Experiments suggest that Minion can noticeably improve performance of applications such as conferencing, virtual private networking, and web browsing, while incurring minimal CPU or bandwidth costs.
Edit intent: fluency
Original: We study the asymptotic performance of two overlaid wireless ad-hoc networks that utilize the same temporal, spectral, and spatial resources based on random access schemes.
Revised: We study the asymptotic performance of two multi-hop overlaid ad-hoc networks that utilize the same temporal, spectral, and spatial resources based on random access schemes.
Edit intent: clarity
Original:  Both networks are decentralized and deploy ALOHA protocols where the secondary nodes are equipped with range-limited perfect spectrum sensors to monitor and protect primary transmissions.
Revised:  Both networks are decentralized and deploy ALOHA protocols where the secondary nodes are equipped with range-limited perfect spectrum sensors to monitor and protect primary transmissions.
Edit intent: fluency
Original:  We thus introduce a new criterion, termed the asymptotic multiplexing gain , which captures the effect of spectrum sensing and inter-network interferences.
Revised:  We thus introduce a new criterion, termed the asymptotic multiplexing gain , which captures the effect of spectrum sensing and inter-network interferences.
Edit intent: fluency
Original: In [Huang-Raskind 2009], the authors proved that the discrete logarithm problem in a prime finite field is random polynomial time equivalent to computing the ramification signature of a real quadric field.
Revised: In [Huang-Raskind 2009], the authors proved that the discrete logarithm problem in a prime finite field is random polynomial time equivalent to computing the ramification signature of a real quadratic field.
Edit intent: clarity
Original: This paper introduces a novel algorithm for the nonnegative matrix factorization and completion problem, which aims to find nonnegative  matrices X and Y from a subset of entries of a nonnegative matrix M so that XY approximates M . This problem is closely related to the two existing problems:  nonnegative matrix factorization and low-rank matrix completion , in the sense that it kills two birds with one stone.
Revised: This paper introduces an algorithm for the nonnegative matrix factorization and completion problem, which aims to find nonnegative matrices X and Y from a subset of entries of a nonnegative matrix M so that XY approximates M . This problem is closely related to the two existing problems: nonnegative matrix factorization and low-rank matrix completion , in the sense that it kills two birds with one stone.
Edit intent: clarity
Original: This paper introduces a novel algorithm for the nonnegative matrix factorization and completion problem, which aims to find nonnegative  matrices X and Y from a subset of entries of a nonnegative matrix M so that XY approximates M . This problem is closely related to the two existing problems:  nonnegative matrix factorization and low-rank matrix completion , in the sense that it kills two birds with one stone.
Revised: This paper introduces a novel algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative matrices X and Y from a subset of entries of a nonnegative matrix M so that XY approximates M . This problem is closely related to the two existing problems: nonnegative matrix factorization and low-rank matrix completion , in the sense that it kills two birds with one stone.
Edit intent: clarity
Original: This paper introduces a novel algorithm for the nonnegative matrix factorization and completion problem, which aims to find nonnegative  matrices X and Y from a subset of entries of a nonnegative matrix M so that XY approximates M . This problem is closely related to the two existing problems:  nonnegative matrix factorization and low-rank matrix completion , in the sense that it kills two birds with one stone.
Revised: This paper introduces a novel algorithm for the nonnegative matrix factorization and completion problem, which aims to find nonnegative matrices X and Y from a subset of entries of a nonnegative matrix M so that XY approximates M . This problem aggregates two existing problems: nonnegative matrix factorization and low-rank matrix completion , in the sense that it kills two birds with one stone.
Edit intent: clarity
Original:  As it takes advantages of both nonnegativity and low rank, its results can be superior than those of the two problems alone.
Revised:  As it takes advantages of both nonnegativity and low-rankness, one can generally obtain superior results than those of the two problems alone.
Edit intent: clarity
Original:  Our algorithm is applied to minimizing a non-convex constrained least-squares formulation and is based on the classic alternating direction augmented Lagrangian method.
Revised:  Our algorithm is applied to minimizing a non-convex constrained least-squares problem using an algorithm based on the classic alternating direction augmented Lagrangian method.
Edit intent: clarity
Original:  Preliminary convergence properties  and numerical simulation results are presented.
Revised:  Preliminary convergence properties of the algorithm and numerical simulation results are presented.
Edit intent: clarity
Original:  Compared to a recent algorithm for nonnegative random matrix factorization, the proposed algorithm yields comparable factorization through accessing only half of the matrix entries.
Revised:  Compared to a recent algorithm for nonnegative matrix factorization, the proposed algorithm yields comparable factorization through accessing only half of the matrix entries.
Edit intent: clarity
Original:  Compared to a recent algorithm for nonnegative random matrix factorization, the proposed algorithm yields comparable factorization through accessing only half of the matrix entries.
Revised:  Compared to a recent algorithm for nonnegative random matrix factorization, the proposed algorithm produces factorizations of similar quality using only about half of the matrix entries.
Edit intent: clarity
Original:  On tasks of recovering incomplete grayscale and hyperspectral images, the results of the proposed algorithm have overall better qualities than those of two recent algorithms for matrix completion .
Revised:  On tasks of recovering incomplete grayscale and hyperspectral images, the proposed algorithm yields overall better qualities than those of two recent algorithms for matrix completion .
Edit intent: clarity
Original:  Here we show that, remarkably, all the properties of all binary projections of the network can be completely traced back to the degree sequence, which is therefore maximally informative.
Revised:  Here we show that, remarkably, the properties of all binary projections of the network can be completely traced back to the degree sequence, which is therefore maximally informative.
Edit intent: coherence
Original: In this sequel to a companion paper  ] , we complement our analysis of the binary projections of the International Trade Network (ITN) by considering its weighted representations.
Revised: In this sequel to a companion paper ]) , we complement our analysis of the binary projections of the International Trade Network (ITN) by considering its weighted representations.
Edit intent: fluency
Original:  and we present a 3 ? 3 prototype FPGA fabricated in 65 nm CMOS. Lastly we present experiments to test the high speed asynchronous configuration chain and evaluate how far our objectives have been achieved with proposed solutions, and we conclude with emphasis on complementary FPGA CAD algorithms, and the effect of CMOS variation on Side-Channel Vulnerability.
Revised:  and we present a 3 X 3 prototype FPGA fabricated in 65 nm CMOS. Lastly we present experiments to test the high speed asynchronous configuration chain and evaluate how far our objectives have been achieved with proposed solutions, and we conclude with emphasis on complementary FPGA CAD algorithms, and the effect of CMOS variation on Side-Channel Vulnerability.
Edit intent: fluency
Original: Robust advances in interactome analysis demand comprehensive, non-redundant , consistently annotated datasets.
Revised: Robust advances in interactome analysis demand comprehensive, non-redundant and consistently annotated datasets.
Edit intent: fluency
Original:  We have developed ppiTrim, a script that can process iRefIndex to produce a consolidated dataset of physical interactions for, in principle, every available organism.
Revised:  We have developed ppiTrim, a script that processes iRefIndex to produce a consolidated dataset of physical interactions for, in principle, every available organism.
Edit intent: clarity
Original:  We have developed ppiTrim, a script that can process iRefIndex to produce a consolidated dataset of physical interactions for, in principle, every available organism.
Revised:  We have developed ppiTrim, a script that can process iRefIndex to produce non-redundant, consistently annotated datasets of physical interactions for, in principle, every available organism.
Edit intent: clarity
Original:  For the current publication we processed only the three largest  datasets: yeast, human and fruitfly. ppiTrim maps interactants to NCBI Gene IDs, deflates possibly spoke-expanded complexes and reconciles annotation labels between different source databases.
Revised:  For the current publication we processed only the three largest organismal datasets: yeast, human and fruitfly. ppiTrim maps interactants to NCBI Gene IDs, deflates possibly spoke-expanded complexes and reconciles annotation labels between different source databases.
Edit intent: clarity
Original:  How this capability can be quantified and related to the functional complexity of an organism remains a challenging problem, in particular since their functional complexity is not well-defined.
Revised:  How this capability can be quantified and related to the functional complexity of an organism remains a challenging problem, in particular since organismal functional complexity is not well-defined.
Edit intent: clarity
Original:  As the agent adapts by increasing its "fit" to the world, information integration and processing increase commensurately along the evolutionary line of descent.
Revised:  As the animat adapts by increasing its "fit" to the world, information integration and processing increase commensurately along the evolutionary line of descent.
Edit intent: clarity
Original:  The correlation of fitness with information integration and with processing measures implies that high fitness requires both information processing as well as integration, but that information integration is a better measure when the task requires memory.
Revised:  We suggest that the correlation of fitness with information integration and with processing measures implies that high fitness requires both information processing as well as integration, but that information integration is a better measure when the task requires memory.
Edit intent: clarity
Original:  The correlation of fitness with information integration and with processing measures implies that high fitness requires both information processing as well as integration, but that information integration is a better measure when the task requires memory.
Revised:  The correlation of fitness with information integration and with processing measures implies that high fitness requires both information processing as well as integration, but that information integration may be a better measure when the task requires memory.
Edit intent: clarity
Original:  A correlation of measures of information integration (but also information processing) and fitness strongly suggests that these measures reflect the functional complexity of the agent , and that such measures can be used to quantify functional complexity even in the absence of fitness data 
Revised:  A correlation of measures of information integration (but also information processing) and fitness strongly suggests that these measures reflect the functional complexity of the animat , and that such measures can be used to quantify functional complexity even in the absence of fitness data 
Edit intent: clarity
Original:  A correlation of measures of information integration (but also information processing) and fitness strongly suggests that these measures reflect the functional complexity of the agent , and that such measures can be used to quantify functional complexity even in the absence of fitness data 
Revised:  A correlation of measures of information integration (but also information processing) and fitness strongly suggests that these measures reflect the functional complexity of the agent , and that such measures can be used to quantify functional complexity even in the absence of fitness data .
Edit intent: fluency
Original: Since the work of E. Noether and H. Weyl in the first half of last century , physics is governed by symmetries and by the geodesic principle, a consequence of symmetries .
Revised: Symmetries play a major role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century , physics is governed by symmetries and by the geodesic principle, a consequence of symmetries .
Edit intent: coherence
Original: Since the work of E. Noether and H. Weyl in the first half of last century , physics is governed by symmetries and by the geodesic principle, a consequence of symmetries .
Revised: Since the work of E. Noether and H. Weyl in the first half of last century .
Edit intent: coherence
Original:  Herein, we briefly review the role of the latter by showing how it allows to conceptually move from classical to relativistic and quantum physics by means of symmetry changes .
Revised:  Herein, we briefly review their role by recalling how symmetry changes allow to conceptually move from classical to relativistic and quantum physics by means of symmetry changes .
Edit intent: clarity
Original:  Herein, we briefly review the role of the latter by showing how it allows to conceptually move from classical to relativistic and quantum physics by means of symmetry changes .
Revised:  Herein, we briefly review the role of the latter by showing how it allows to conceptually move from classical to relativistic and quantum physics .
Edit intent: clarity
Original:  This improves our previous best bounds with Moser and Scheder [2011] for 3-SAT from O(1.32065^n) to O( 1.30704 ^n) and for 4-SAT from O(1.46928^n) to O( 1.46899 ^n).
Revised:  This improves our previous best bounds with Moser and Scheder [2011] for 3-SAT to O( 1.30704 ^n) and for 4-SAT from O(1.46928^n) to O( 1.46899 ^n).
Edit intent: clarity
Original: Bell's theorem \mbox{ Bel19640pt \mbox{ CHSH1969 }0pt } basically states that local hidden variable theory cannot predict the correlations produced by quantum mechanics.
Revised: Bell's theorem 0pt \mbox{ CHSH1969 }0pt } basically states that local hidden variable theory cannot predict the correlations produced by quantum mechanics.
Edit intent: clarity
Original:  We establish a new paradigm that departs completely from Bell's paradigm .
Revised:  We establish a new paradigm that departs from Bell's paradigm .
Edit intent: clarity
Original:  We assume that there are no choices for Alice and Bob and  the measurements Alice and Bob will make are prescribed from the start.
Revised:  We assume that there are no choices for Alice and Bob and that the measurements Alice and Bob will make are prescribed from the start.
Edit intent: fluency
Original:  We assume that there are no choices for Alice and Bob and  the measurements Alice and Bob will make are prescribed from the start.
Revised:  We assume that there are no choices for Alice and Bob and the measurements Alice and Bob will make are fixed from the start.
Edit intent: clarity
Original: Passive molecular movements in cells are often claimed to exhibit "anomalous subdiffusion", where the mean-squared displacement (MSD) scales as a power law of time with exponent \alpha< 1. Diffusion hindrance by obstacles is often invoked to explain these observations.
Revised: In vivo measurements of the passive movements of biomolecules or vesicles in cells consistently report ''anomalous diffusion'', where mean-squared displacement (MSD) scales as a power law of time with exponent \alpha< 1. Diffusion hindrance by obstacles is often invoked to explain these observations.
Edit intent: clarity
Original: Passive molecular movements in cells are often claimed to exhibit "anomalous subdiffusion", where the mean-squared displacement (MSD) scales as a power law of time with exponent \alpha< 1. Diffusion hindrance by obstacles is often invoked to explain these observations.
Revised: Passive molecular movements in cells are often claimed to exhibit "anomalous subdiffusion", where the mean-squared displacements scale as a power law of time with exponent \alpha< 1. Diffusion hindrance by obstacles is often invoked to explain these observations.
Edit intent: clarity
Original:  This is however at odds with the theoretical support for hindered diffusion among randomly located immobile obstacles, which predicts that true subdiffusion occurs only in the vicinity of the threshold for the percolation of obstacles, and that \alpha takes a%DIFDELCMD < {\it %DIFDELCMD < %%% unique , universal value .
Revised:  This is however at odds with the theoretical support for hindered diffusion among randomly located immobile obstacles, which predicts that true subdiffusion occurs only in the vicinity of the threshold for the percolation of obstacles, and that \alpha takes a%DIFDELCMD < {\it %DIFDELCMD < %%% , universal value .
Edit intent: coherence