wanyu/IteraTeR_v2 huggingface dataset:
Original: Recent results establish for 2-spin antiferromagnetic systems that the computational complexity of approximating the partition function on graphs of maximum degree D undergoes a phase transition that coincides with the uniqueness /non-uniqueness phase transition on the infinite D-regular tree.
Revised: Recent results establish for 2-spin antiferromagnetic systems that the computational complexity of approximating the partition function on graphs of maximum degree D undergoes a phase transition that coincides with the uniqueness phase transition on the infinite D-regular tree.
Edit intent: clarity
Original:  We then prove for all temperatures below this critical temperature (the region where the ordered phase "dominates") that it is #BIS-hard to approximate the partition function on bipartite graphs of maximum degree D.
Revised:  We then prove for all temperatures below this critical temperature that it is #BIS-hard to approximate the partition function on bipartite graphs of maximum degree D.
Edit intent: clarity
Original:  The analysis of these random graphs relies on recent results establishing connections between the maxima of the expectation of their partition function, attractive fixpoints of the associated tree recursions, and induced matrix norms.
Revised:  The analysis of these random graphs relies on recent connections between the maxima of the expectation of their partition function, attractive fixpoints of the associated tree recursions, and induced matrix norms.
Edit intent: clarity
Original:  In this paper we extend these connections to random regular graphs for all ferromagnetic models . Using these connections, we establish the Bethe prediction for every ferromagnetic spin system on random regular graphs.
Revised:  We extend these connections to random regular graphs for all ferromagnetic models . Using these connections, we establish the Bethe prediction for every ferromagnetic spin system on random regular graphs.
Edit intent: coherence
Original:  In this paper we extend these connections to random regular graphs for all ferromagnetic models . Using these connections, we establish the Bethe prediction for every ferromagnetic spin system on random regular graphs.
Revised:  In this paper we extend these connections to random regular graphs for all ferromagnetic models and establish the Bethe prediction for every ferromagnetic spin system on random regular graphs.
Edit intent: coherence
Original:  As a further consequence, we prove for the ferromagnetic Potts model that the Swendsen-Wang algorithm is torpidly mixing on random D-regular graphs at the critical temperature for sufficiently large q.
Revised:  We also prove for the ferromagnetic Potts model that the Swendsen-Wang algorithm is torpidly mixing on random D-regular graphs at the critical temperature for sufficiently large q.
Edit intent: coherence
Original:  As a further consequence, we prove for the ferromagnetic Potts model that the Swendsen-Wang algorithm is torpidly mixing on random D-regular graphs at the critical temperature for sufficiently large q.
Revised:  As a further consequence, we prove for the ferromagnetic Potts model that the Swendsen-Wang algorithm is torpidly mixing on random D-regular graphs at the critical temperature for large q.
Edit intent: clarity
Original: Various types of pooled annuity funds that enable a group of individuals to pool their mortality risk have been proposed in the literature.
Revised: Various types of structures that enable a group of individuals to pool their mortality risk have been proposed in the literature.
Edit intent: clarity
Original:  We show that, with a finite number of members in the fund, the group self-annuitization scheme is not actuarially fair: some members subsidise the other members.
Revised:  We show that, with a finite number of members in the fund, the group self-annuitization scheme is not actuarially fair: some members subsidize the other members.
Edit intent: fluency
Original:  The implication is that the members who are subsidising the others may obtain a higher expected benefit by joining a fund with a more favourable membership profile.
Revised:  The implication is that the members who are subsidizing the others may obtain a higher expected benefit by joining a fund with a more favourable membership profile.
Edit intent: fluency
Original:  Since the pooled annuity funds propose different methods of pooling mortality risk, we investigate the connections between them and find that they are genuinely different for a finite heterogeneous membership profile .
Revised:  However, we find that the subsidies are financially significant only for very small or highly heterogeneous membership profiles .
Edit intent: coherence
Original:  The players  objective is to maximize the probability that their outputs satisfy a+b=xy in F_q. This game was introduced by Buhrman and Massar ( Phys.
Revised:  The players ' objective is to maximize the probability that their outputs satisfy a+b=xy in F_q. This game was introduced by Buhrman and Massar ( Phys.
Edit intent: fluency
Original:  Rev. A 72.5 ( 2005) ) as a large alphabet generalization of the CHSH game, which is one of the most well-studied  games in quantum information theory, and which has  large number of applications to quantum cryptography and quantum complexity.
Revised:  Rev. A 72.5 ( 2005) as a large alphabet generalization of the CHSH game, which is one of the most well-studied games in quantum information theory, and which has large number of applications to quantum cryptography and quantum complexity.
Edit intent: fluency
Original:  Rev. A 72.5 ( 2005) ) as a large alphabet generalization of the CHSH game, which is one of the most well-studied  games in quantum information theory, and which has  large number of applications to quantum cryptography and quantum complexity.
Revised:  Rev. A 72.5 ( 2005) ) as a large alphabet generalization of the celebrated CHSH game---which is one of the most well-studied games in quantum information theory, and which has large number of applications to quantum cryptography and quantum complexity.
Edit intent: clarity
Original:  Rev. A 72.5 ( 2005) ) as a large alphabet generalization of the CHSH game, which is one of the most well-studied  games in quantum information theory, and which has  large number of applications to quantum cryptography and quantum complexity.
Revised:  Rev. A 72.5 ( 2005) ) as a large alphabet generalization of the CHSH game, which is one of the most well-studied games in quantum information theory, and which has a large number of applications to quantum cryptography and quantum complexity.
Edit intent: fluency
Original:  In this work, we obtain the first asymptotic results on the quantum and classical values of CHSH_q . The main result regarding the quantum value of CHSH_q is an upper bound of O(q^{-1/2).
Revised:  Our main contributions in this paper are the first asymptotic results on the quantum and classical values of CHSH_q . The main result regarding the quantum value of CHSH_q is an upper bound of O(q^{-1/2).
Edit intent: clarity
Original:  In this work, we obtain the first asymptotic results on the quantum and classical values of CHSH_q . The main result regarding the quantum value of CHSH_q is an upper bound of O(q^{-1/2).
Revised:  In this work, we obtain the first asymptotic results on the quantum and classical values of CHSH_q ).
Edit intent: coherence
Original:  the length of this longest edge is known as %DIFDELCMD < {\em %%% bottleneck .
Revised:  the length of this longest edge is known as %DIFDELCMD < {\em %%% bottleneck .
Edit intent: fluency
Original:  Then we extend our idea toward another approximation algorithm which computes a plane matching of size at least 2n{5} whose edges have length at most 2 3 times the bottleneck . Both algorithms have a time complexity of O(n^{1.5\sqrt{\log n})} .
Revised:  Then we extend our idea toward an O(n\log n)-time approximation algorithm which computes a plane matching of size at least 2n{5} whose edges have length at most 2 3 times the bottleneck . Both algorithms have a time complexity of O(n^{1.5\sqrt{\log n})} .
Edit intent: clarity
Original:  Then we extend our idea toward another approximation algorithm which computes a plane matching of size at least 2n{5} whose edges have length at most 2 3 times the bottleneck . Both algorithms have a time complexity of O(n^{1.5\sqrt{\log n})} .
Revised:  Then we extend our idea toward another approximation algorithm which computes a plane matching of size at least 2n{5} whose edges have length at most 2 3 times the bottleneck \sqrt{\log n})} .
Edit intent: coherence
Original:  the length of this longest edge is known as bottleneck {\em  .
Revised:  the length of this longest edge is known as {\em .
Edit intent: clarity
Original: The fast directional algorithm (FDA) proposed in 1%DIFDELCMD < ] %%% is a wideband and highly efficient kernel independent algorithm for oscillatory kernels.
Revised:  1%DIFDELCMD < ] %%% is a wideband and highly efficient kernel independent algorithm for oscillatory kernels.
Edit intent: coherence
Original: The fast directional algorithm (FDA) proposed in 1%DIFDELCMD < ] %%% is a wideband and highly efficient kernel independent algorithm for oscillatory kernels.
Revised: The fast directional algorithm (FDA) proposed in %DIFDELCMD < ] %%% is a wideband and highly efficient kernel independent algorithm for oscillatory kernels.
Edit intent: clarity
Original: The fast directional algorithm (FDA) proposed in 1%DIFDELCMD < ] %%% is a wideband and highly efficient kernel independent algorithm for oscillatory kernels.
Revised: The fast directional algorithm (FDA) proposed in 1%DIFDELCMD < ] %%% 
Edit intent: coherence
Original:  In this paper, the FDA is adapted to accelerate acoustic boundary element method (BEM) for solving  Burton-Miller boundary integral equation (BIE) .
Revised:  In this paper, a highly efficient fast boundary element method (BEM) for solving Burton-Miller boundary integral equation (BIE) .
Edit intent: clarity
Original: We review pro and contra of the hypothesis that generic polymer properties of topological constraints are behind many aspects of chromatin folding in eukaryote cells.
Revised: We review pro and contra of the hypothesis that generic polymer properties of topological constraints are behind many aspects of chromatin folding in eukaryotic cells.
Edit intent: fluency
Original: The computational complexity of the solution h to the ordinary differential equation h(0)=0, h'(t) = g(t, h(t)) under various assumptions on the function g has been investigated.
Revised: The computational complexity of the solutions h to the ordinary differential equation h(0)=0, h'(t) = g(t, h(t)) under various assumptions on the function g has been investigated.
Edit intent: fluency
Original: The fundamental concepts of the Unified Growth Theory , the three stages of growth (Malthusian Regime, Post-Malthusian Regime and Modern Growth Regime) are contradicted by data.
Revised: The Unified Growth Theory , the three stages of growth (Malthusian Regime, Post-Malthusian Regime and Modern Growth Regime) are contradicted by data.
Edit intent: clarity
Original: The Unified Growth Theory is a story based firmly on illusions created by hyperbolic distributions.
Revised: The Unified Growth Theory is a puzzling collection of myths based on illusions created by hyperbolic distributions.
Edit intent: clarity
Original:  All elaborate explanations revolving around these phantom features represent an interesting story but they are scientifically unacceptable and, therefore , they do not explain the economic growth.
Revised:  All elaborate explanations revolving around phantom features created by hyperbolic illusions might be fascinating but they are scientifically unacceptable and, therefore , they do not explain the economic growth.
Edit intent: clarity
Original:  All elaborate explanations revolving around these phantom features represent an interesting story but they are scientifically unacceptable and, therefore , they do not explain the economic growth.
Revised:  All elaborate explanations revolving around these phantom features represent an interesting story but they are scientifically unacceptable and, consequently , they do not explain the economic growth.
Edit intent: coherence
Original:  The data clearly indicate that the economic growth was not as complicated and untidy as incorrectly described by the Unified Growth Theory but elegantly simple.
Revised:  The data clearly indicate that the economic growth was not as complicated as described by the Unified Growth Theory but elegantly simple.
Edit intent: clarity
Original:  The reconstruction of the phylogenetic tree topology of four taxa is, still nowadays, one of the main challenges in phylogenetics.
Revised: Background: The reconstruction of the phylogenetic tree topology of four taxa is, still nowadays, one of the main challenges in phylogenetics.
Edit intent: coherence
Original:   In this paper we consider an expectation-maximization method for maximizing the likelihood of ( discrete-time, non-homogeneous ) evolutionary Markov models on trees.
Revised:  Results: In this paper we consider an expectation-maximization method for maximizing the likelihood of ( discrete-time, non-homogeneous ) evolutionary Markov models on trees.
Edit intent: fluency
Original:   In this paper we consider an expectation-maximization method for maximizing the likelihood of ( discrete-time, non-homogeneous ) evolutionary Markov models on trees.
Revised:  In this paper we consider an expectation-maximization method for maximizing the likelihood of ( time nonhomogeneous ) evolutionary Markov models on trees.
Edit intent: clarity
Original:  Our results show that the method proposed here outperforms Neighbor-Joining and the usual  maximum likelihood methods (which assume the same evolutionary rates across lineages) on 4-leaf trees that do not satisfy homogeneity across lineages.
Revised:  Our results show that the method proposed here outperforms neighbor-joining and the usual maximum likelihood methods (which assume the same evolutionary rates across lineages) on 4-leaf trees that do not satisfy homogeneity across lineages.
Edit intent: fluency
Original: We present a deterministic polynomial-time algorithm which computes the multilinear factors of multivariate lacunary polynomials over number fields.
Revised: We present a deterministic algorithm which computes the multilinear factors of multivariate lacunary polynomials over number fields.
Edit intent: clarity
Original:  It is based on a new Gap theorem which allows to test whether P(X)=j=1^k a_j X^{\alpha_j(vX+t)^{\beta_j}(uX+w)^{\gamma_j} is identically zero in polynomial time.
Revised:  (vX+t)^{\beta_j}(uX+w)^{\gamma_j} is identically zero in polynomial time.
Edit intent: coherence
Original:  We also give a version of our Gap Theorem valid for fields of large characteristic, and deduce a randomized polynomial-time algorithm to compute multilinear factors with at least three monomials of multivariate lacunary polynomialsof finite fields of large characteristic.
Revised:  We also give a version of our Gap Theorem valid for fields of large characteristic, our algorithms compute the multilinear factors having at least three monomials of multivariate lacunary polynomialsof finite fields of large characteristic.
Edit intent: clarity
Original:  Recently, more general \Lambda - and \Xi-coalescents have been observed to provide better modelling fits to some genetic data sets.
Revised:  Recently, more general \Lambda -- and \Xi--coalescents have been observed to provide better modelling fits to some genetic data sets.
Edit intent: fluency
Original:  We derive families of approximate CSDs for finite sites \Lambda - and \Xi-coalescents , and use them to obtain "approximately optimal" IS and PAC algorithms for \Lambda -coalescents , yielding substantial gains in efficiency over existing methods.
Revised:  We derive families of approximate CSDs for finite sites \Lambda -- and \Xi--coalescents , and use them to obtain "approximately optimal" IS and PAC algorithms for \Lambda -coalescents , yielding substantial gains in efficiency over existing methods.
Edit intent: fluency
Original:  We derive families of approximate CSDs for finite sites \Lambda - and \Xi-coalescents , and use them to obtain "approximately optimal" IS and PAC algorithms for \Lambda -coalescents , yielding substantial gains in efficiency over existing methods.
Revised:  We derive families of approximate CSDs for finite sites \Lambda - and \Xi-coalescents , and use them to obtain "approximately optimal" IS and PAC algorithms for \Lambda --coalescents , yielding substantial gains in efficiency over existing methods.
Edit intent: fluency
Original:  Recently, more general \Lambda -- and \Xi--coalescents have been observed to provide better modelling fits to some genetic data sets.
Revised:  Recently, more general \Lambda - and \Xi-coalescents have been observed to provide better modelling fits to some genetic data sets.
Edit intent: fluency
Original:  We derive families of approximate CSDs for finite sites \Lambda -- and \Xi--coalescents , and use them to obtain "approximately optimal" IS and PAC algorithms for \Lambda --coalescents , yielding substantial gains in efficiency over existing methods.
Revised:  We derive families of approximate CSDs for finite sites \Lambda - and \Xi-coalescents , and use them to obtain "approximately optimal" IS and PAC algorithms for \Lambda --coalescents , yielding substantial gains in efficiency over existing methods.
Edit intent: fluency
Original:  We derive families of approximate CSDs for finite sites \Lambda -- and \Xi--coalescents , and use them to obtain "approximately optimal" IS and PAC algorithms for \Lambda --coalescents , yielding substantial gains in efficiency over existing methods.
Revised:  We derive families of approximate CSDs for finite sites \Lambda -- and \Xi--coalescents , and use them to obtain "approximately optimal" IS and PAC algorithms for \Lambda -coalescents , yielding substantial gains in efficiency over existing methods.
Edit intent: fluency
Original:  Without any modifications, this method can be applied to weighted automata over a commutative semiring .
Revised:  Without any modifications, this method can be applied to weighted automata over commutative semirings .
Edit intent: fluency
Original: In this paper we study how certain families of aperiodic infinite words can be used to produce aperiodic pseudorandom number generators (PRNGs) with good statistical behaviour .
Revised: In this paper we study how certain families of aperiodic infinite words can be used to produce aperiodic pseudorandom number generators (PRNGs) with good statistical behavior .
Edit intent: fluency
Original:  We introduce the well distributed occurrences (WELLDOC) combinatorial property for infinite words, which guarantees good behavior -- absence of the lattice structure defect in related pseudorandom number generators.
Revised:  We introduce the well distributed occurrences (WELLDOC) combinatorial property for infinite words, which guarantees good behavior -- absence of the lattice structure defect in related pseudorandom number generators.
Edit intent: fluency
Original:  We introduce the well distributed occurrences (WELLDOC) combinatorial property for infinite words, which guarantees good behavior -- absence of the lattice structure defect in related pseudorandom number generators.
Revised:  We introduce the well distributed occurrences (WELLDOC) combinatorial property for infinite words, which guarantees absence of the lattice structure defect in related pseudorandom number generators.
Edit intent: clarity
Original: A novel architecture of a recurrent neural network (RNN) , integrated with a fully-connected deep neural network (DNN) as its feature extractor , is presented.
Revised: We present an architecture of a recurrent neural network (RNN) , integrated with a fully-connected deep neural network (DNN) as its feature extractor , is presented.
Edit intent: clarity
Original: A novel architecture of a recurrent neural network (RNN) , integrated with a fully-connected deep neural network (DNN) as its feature extractor , is presented.
Revised: A novel architecture of a recurrent neural network (RNN) with a fully-connected deep neural network (DNN) as its feature extractor , is presented.
Edit intent: clarity
Original:  We describe a primal-dual training method that formulates learning RNNs as a formal optimization problem with an inequality constraint that guarantees stability of the network dynamics.
Revised:  The focus of this paper is a primal-dual training method that formulates learning RNNs as a formal optimization problem with an inequality constraint that guarantees stability of the network dynamics.
Edit intent: clarity
Original:  We describe a primal-dual training method that formulates learning RNNs as a formal optimization problem with an inequality constraint that guarantees stability of the network dynamics.
Revised:  We describe a primal-dual training method that formulates the learning of the RNN as a formal optimization problem with an inequality constraint that guarantees stability of the network dynamics.
Edit intent: clarity
Original:  Experimental results demonstrate the effectiveness of this new method, which achieves 18.86\% phone recognition error on the TIMIT benchmark with the core test set.
Revised:  Experimental results demonstrate the effectiveness of this new method, which achieves 18.86\% phone recognition error on the TIMIT benchmark for the core test set.
Edit intent: clarity
Original:  Parcels are the basic spatial units for fine-scale urban modeling and urban studies, as well as carrying out spatial plans.
Revised:  Parcels are the basic spatial units for fine-scale urban modeling , urban studies, as well as carrying out spatial plans.
Edit intent: fluency
Original:  Vector cellular automata models were developed for each city to select urban parcels from all generated parcels .
Revised:  Vector cellular automata models were developed for each city to select urban parcels .
Edit intent: clarity
Original:  The method for automated identification and characterization of parcels was used in China with 82,645 urban parcels generating in 297 cities .
Revised:  The method is applied to the entire state of China and identifies 82,645 urban parcels generating in 297 cities .
Edit intent: clarity
Original:  The method for automated identification and characterization of parcels was used in China with 82,645 urban parcels generating in 297 cities .
Revised:  The method for automated identification and characterization of parcels was used in China with 82,645 urban parcels in 297 cities .
Edit intent: clarity
Original: Aiming at the paucity of urban parcels in developing countries in general and Chinain particular , this paper proposes a method to automatically identify and characterize parcels (AICP) with ubiquitous available OpenStreetMap (OSM) and Points of Interest ( POIs) . Parcels are the basic spatial units for fine-scale urban modeling, urban studies, as well as spatial planning.
Revised: Against the paucity of urban parcels in developing countries in general and Chinain particular , this paper proposes a method to automatically identify and characterize parcels (AICP) with ubiquitous available OpenStreetMap (OSM) and Points of Interest ( POIs) . Parcels are the basic spatial units for fine-scale urban modeling, urban studies, as well as spatial planning.
Edit intent: coherence
Original: Aiming at the paucity of urban parcels in developing countries in general and Chinain particular , this paper proposes a method to automatically identify and characterize parcels (AICP) with ubiquitous available OpenStreetMap (OSM) and Points of Interest ( POIs) . Parcels are the basic spatial units for fine-scale urban modeling, urban studies, as well as spatial planning.
Revised: Aiming at the paucity of urban parcels in China , this paper proposes a method to automatically identify and characterize parcels (AICP) with ubiquitous available OpenStreetMap (OSM) and Points of Interest ( POIs) . Parcels are the basic spatial units for fine-scale urban modeling, urban studies, as well as spatial planning.
Edit intent: clarity