wanyu/IteraTeR_v2 huggingface dataset:
Original:  The proposed approach achieves a significant improvement in performance in the lyrics transcription and alignment tasks on several well-known polyphonic test datasets , outperforming all comparable existing systems .
Revised:  The proposed approach achieves a significant improvement in performance in the lyrics transcription and alignment tasks on several well-known polyphonic test datasets .
Edit intent: clarity
Original:  To cope with this issue, we propose a novel approach named temporal heterogeneous graph convolutional network (THGCN) . THGCN first embeds both spatial information and node attribute information together.
Revised:  To cope with this issue, we propose a novel approach named temporal heterogeneous graph convolutional network (THGCN) . 
Edit intent: coherence
Original: In Bayesian inference, we seek to compute information about random variables such as moments or quantiles on the basis of data and prior information.
Revised: In Bayesian inference, we seek to compute information about random variables such as moments or quantiles on the basis of available data and prior information.
Edit intent: clarity
Original:  When the distribution of random variables is complicated , Monte Carlo (MC) sampling is usually required.
Revised:  When the distribution of random variables is intractable , Monte Carlo (MC) sampling is usually required.
Edit intent: clarity
Original:  Importance sampling is a standard MC tool for addressing this problem: one generates a collection of samples according to an importance distribution, computes their contribution to an unnormalized density, i.e., the importance weight, and then sums the result followed by normalization.
Revised:  Importance sampling is a standard MC tool that approximates this unavailable distribution with a set of weighted samples.
Edit intent: clarity
Original:  This procedure is asymptotically consistent as the number of MC samples , and hence deltas (particles) that parameterize the density estimate, go to infinity.
Revised:  This procedure is asymptotically consistent as the number of MC samples (particles) that parameterize the density estimate, go to infinity.
Edit intent: coherence
Original:  This procedure is asymptotically consistent as the number of MC samples , and hence deltas (particles) that parameterize the density estimate, go to infinity.
Revised:  This procedure is asymptotically consistent as the number of MC samples , and hence deltas (particles) go to infinity.
Edit intent: clarity
Original:  However, retaining in infnitely many particles is intractable.
Revised:  However, retaining infinitely many particles is intractable.
Edit intent: fluency
Original:  Thus, we propose a scheme for only keeping a nite representative subset\emph{ of particles and their augmented importance weights that is nearly consistent } .
Revised:  Thus, we propose a way to only keep a\emph{ of particles and their augmented importance weights that is nearly consistent } .
Edit intent: clarity
Original:  Thus, we propose a scheme for only keeping a nite representative subset\emph{ of particles and their augmented importance weights that is nearly consistent } .
Revised:  Thus, we propose a scheme for only keeping a nite representative subset\emph{ of particles and their augmented importance weights that is nearly consistent } .
Edit intent: fluency
Original:  Thus, we propose a scheme for only keeping a nite representative subset\emph{ of particles and their augmented importance weights that is nearly consistent } .
Revised:  Thus, we propose a scheme for only keeping a nite representative subset\emph{ of particles and their augmented importance weights that is nearly consistent. To do so in } .
Edit intent: coherence
Original: We describe an approach for modeling  concentration profiles in grid-based microfluidic chips for fluid mixing.
Revised: We describe an approach for modeling fluid concentration profiles in grid-based microfluidic chips for fluid mixing.
Edit intent: fluency
Original:  This approach provides an algorithm that accurately predicts fluid concentrations at the chip outlets.
Revised:  This approach provides an algorithm that predicts fluid concentrations at the chip outlets.
Edit intent: clarity
Original: An (r, s) -formation is aconcatenation of s permutations of r distinct letters.
Revised: Let up (r, s) -formation is aconcatenation of s permutations of r distinct letters.
Edit intent: clarity
Original:  (Nivasch, 2010) and (Pettie, 2015) found bounds on F_{r, s n +(r-1)(m-1), F_{r,3 ( \le  r-1)  ( m-2), F_{r,2 ) = (n-r)r+2r-1,and F_{r,3 = 2(n-r)r+3r-1, improving on bounds of (Klazar, 1992), (Nivasch, 2010), and (Pettie, 2015).
Revised:  (Nivasch, 2010) and (Pettie, 2015) found bounds on F_{r, s n ( \le r-1) ( m-2), F_{r,2 ) = (n-r)r+2r-1,and F_{r,3 = 2(n-r)r+3r-1, improving on bounds of (Klazar, 1992), (Nivasch, 2010), and (Pettie, 2015).
Edit intent: clarity
Original:  (Nivasch, 2010) and (Pettie, 2015) found bounds on F_{r, s n +(r-1)(m-1), F_{r,3 ( \le  r-1)  ( m-2), F_{r,2 ) = (n-r)r+2r-1,and F_{r,3 = 2(n-r)r+3r-1, improving on bounds of (Klazar, 1992), (Nivasch, 2010), and (Pettie, 2015).
Revised:  (Nivasch, 2010) and (Pettie, 2015) found bounds on F_{r, s n +(r-1)(m-1), F_{r,3 ( \le ( r-1) ( m-2), F_{r,2 ) = (n-r)r+2r-1,and F_{r,3 = 2(n-r)r+3r-1, improving on bounds of (Klazar, 1992), (Nivasch, 2010), and (Pettie, 2015).
Edit intent: fluency
Original:  (Nivasch, 2010) and (Pettie, 2015) found bounds on F_{r, s n +(r-1)(m-1), F_{r,3 ( \le  r-1)  ( m-2), F_{r,2 ) = (n-r)r+2r-1,and F_{r,3 = 2(n-r)r+3r-1, improving on bounds of (Klazar, 1992), (Nivasch, 2010), and (Pettie, 2015).
Revised:  (Nivasch, 2010) and (Pettie, 2015) found bounds on F_{r, s n +(r-1)(m-1), F_{r,3 ( \le r-1) ( m-2), F_{r,2 ) = 2(n-r)r+3r-1, improving on bounds of (Klazar, 1992), (Nivasch, 2010), and (Pettie, 2015).
Edit intent: fluency
Original:  For any sequence u, define Ex(u, n) to be the maximum possible length of a sequence with n distinct letters that avoids u and has every r consecutive letters distinct, where r is the number of distinct letters in u. Klazar proved that Ex( (a_1%DIFDELCMD < \dots %%% a_r)^2 ,n) < (2n+1)L , where L = Ex( (a_1%DIFDELCMD < \dots %DIFDELCMD < %%% a_r)^2 ,K-1)+1 and K = (r-1)^4 + 1. Here we prove that K = (r-1)^4 + 1 in Klazar's bound can be replaced with K = (r-1) ^3 \binom{r}{2} +1.
Revised:  For any sequence u, define Ex(u, n) to be the maximum possible length of a sequence with n distinct letters that avoids u and has every r consecutive letters distinct, where r is the number of distinct letters in u. Klazar proved that Ex( %DIFDELCMD < \dots %%% a_r)^2 ,n) < (2n+1)L , where L = Ex( (a_1%DIFDELCMD < \dots %DIFDELCMD < %%% a_r)^2 ,K-1)+1 and K = (r-1)^4 + 1. Here we prove that K = (r-1)^4 + 1 in Klazar's bound can be replaced with K = (r-1) ^3 \binom{r}{2} +1.
Edit intent: fluency
Original:  For any sequence u, define Ex(u, n) to be the maximum possible length of a sequence with n distinct letters that avoids u and has every r consecutive letters distinct, where r is the number of distinct letters in u. Klazar proved that Ex( (a_1%DIFDELCMD < \dots %%% a_r)^2 ,n) < (2n+1)L , where L = Ex( (a_1%DIFDELCMD < \dots %DIFDELCMD < %%% a_r)^2 ,K-1)+1 and K = (r-1)^4 + 1. Here we prove that K = (r-1)^4 + 1 in Klazar's bound can be replaced with K = (r-1) ^3 \binom{r}{2} +1.
Revised:  For any sequence u, define Ex(u, n) to be the maximum possible length of a sequence with n distinct letters that avoids u and has every r consecutive letters distinct, where r is the number of distinct letters in u. Klazar proved that Ex( (a_1%DIFDELCMD < \dots %%% a_r)^2 ,n) < (2n+1)L where L = Ex( (a_1%DIFDELCMD < \dots %DIFDELCMD < %%% a_r)^2 ,K-1)+1 and K = (r-1)^4 + 1. Here we prove that K = (r-1)^4 + 1 in Klazar's bound can be replaced with K = (r-1) ^3 \binom{r}{2} +1.
Edit intent: fluency
Original:  For any sequence u, define Ex(u, n) to be the maximum possible length of a sequence with n distinct letters that avoids u and has every r consecutive letters distinct, where r is the number of distinct letters in u. Klazar proved that Ex( (a_1%DIFDELCMD < \dots %%% a_r)^2 ,n) < (2n+1)L , where L = Ex( (a_1%DIFDELCMD < \dots %DIFDELCMD < %%% a_r)^2 ,K-1)+1 and K = (r-1)^4 + 1. Here we prove that K = (r-1)^4 + 1 in Klazar's bound can be replaced with K = (r-1) ^3 \binom{r}{2} +1.
Revised:  For any sequence u, define Ex(u, n) to be the maximum possible length of a sequence with n distinct letters that avoids u and has every r consecutive letters distinct, where r is the number of distinct letters in u. Klazar proved that Ex( (a_1%DIFDELCMD < \dots %%% a_r)^2 ,n) < (2n+1)L , where L = Ex( %DIFDELCMD < \dots %DIFDELCMD < %%% a_r)^2 ,K-1)+1 and K = (r-1)^4 + 1. Here we prove that K = (r-1)^4 + 1 in Klazar's bound can be replaced with K = (r-1) ^3 \binom{r}{2} +1.
Edit intent: fluency
Original:  For any sequence u, define Ex(u, n) to be the maximum possible length of a sequence with n distinct letters that avoids u and has every r consecutive letters distinct, where r is the number of distinct letters in u. Klazar proved that Ex( (a_1%DIFDELCMD < \dots %%% a_r)^2 ,n) < (2n+1)L , where L = Ex( (a_1%DIFDELCMD < \dots %DIFDELCMD < %%% a_r)^2 ,K-1)+1 and K = (r-1)^4 + 1. Here we prove that K = (r-1)^4 + 1 in Klazar's bound can be replaced with K = (r-1) ^3 \binom{r}{2} +1.
Revised:  For any sequence u, define Ex(u, n) to be the maximum possible length of a sequence with n distinct letters that avoids u and has every r consecutive letters distinct, where r is the number of distinct letters in u. Klazar proved that Ex( (a_1%DIFDELCMD < \dots %%% a_r)^2 ,n) < (2n+1)L , where L = Ex( (a_1%DIFDELCMD < \dots %DIFDELCMD < %%% up(r,2) ,K-1)+1 and K = (r-1)^4 + 1. Here we prove that K = (r-1)^4 + 1 in Klazar's bound can be replaced with K = (r-1) ^3 \binom{r}{2} +1.
Edit intent: clarity
Original:  For any sequence u, define Ex(u, n) to be the maximum possible length of a sequence with n distinct letters that avoids u and has every r consecutive letters distinct, where r is the number of distinct letters in u. Klazar proved that Ex( (a_1%DIFDELCMD < \dots %%% a_r)^2 ,n) < (2n+1)L , where L = Ex( (a_1%DIFDELCMD < \dots %DIFDELCMD < %%% a_r)^2 ,K-1)+1 and K = (r-1)^4 + 1. Here we prove that K = (r-1)^4 + 1 in Klazar's bound can be replaced with K = (r-1) ^3 \binom{r}{2} +1.
Revised:  For any sequence u, define Ex(u, n) to be the maximum possible length of a sequence with n distinct letters that avoids u and has every r consecutive letters distinct, where r is the number of distinct letters in u. Klazar proved that Ex( (a_1%DIFDELCMD < \dots %%% a_r)^2 ,n) < (2n+1)L , where L = Ex( (a_1%DIFDELCMD < \dots %DIFDELCMD < %%% a_r)^2 ,K-1)+1 , K = (r-1)^4 + 1. Here we prove that K = (r-1)^4 + 1 in Klazar's bound can be replaced with K = (r-1) ^3 \binom{r}{2} +1.
Edit intent: coherence
Original: }\alpha(n)^{t+1} \pm O(\alpha(n)^{t})} for  t \geq 1. Furthermore, we extend the equalities F_{r,2
Revised: }\alpha(n)^{t+1} \pm O(\alpha(n)^{t})} for all t \geq 1. Furthermore, we extend the equalities F_{r,2
Edit intent: clarity
Original:  The algorithm of Vetsigian et al.
Revised:  The model of Vetsigian et al.
Edit intent: clarity
Original:  All the parameters used in the model are varied to assess their impact on achieving universality .
Revised:  All the parameters used in the model are varied to assess their impact on convergence and optimality score .
Edit intent: clarity
Original:  We use this to examine the scaling of the solutions in order to understand the origin of universality and find that there is a direct link to the mutation rate.
Revised:  We use this to examine the scaling of the solutions in order to re-examine universality and find that there is a direct link to the mutation rate.
Edit intent: clarity
Original:  We use this to examine the scaling of the solutions in order to understand the origin of universality and find that there is a direct link to the mutation rate.
Revised:  We use this to examine the scaling of the solutions in order to understand the origin of universality and find that there is a direct link to mutation rate.
Edit intent: fluency
Original: Binary decisions are the simplest type of decisions that we make in our everyday lives.
Revised: Binary decisions are the simplest form of decisions that we make in our everyday lives.
Edit intent: clarity
Original: Binary decisions are the simplest type of decisions that we make in our everyday lives.
Revised: Binary decisions are the simplest type of decisions that are made in our daily lives.
Edit intent: fluency
Original:  These decisions are also made by computers, machines and  electronic components.
Revised:  These decisions are also made by computers, machines and various electronic components.
Edit intent: clarity
Original:  Here we present a simple framework to implement binary decisions using one or many qubits  .
Revised:  Here we present a simple framework to implement binary decisions using one or many qubits is presented .
Edit intent: clarity
Original:  These structured solvers are based on variations of the classical L-shaped and progressive-hedging methods .
Revised:  These structured solvers are based on variations of the classical L-shaped and progressive-hedging algorithms .
Edit intent: clarity
Original:  We provide concise mathematical backgrounds for the various tools and constructs available in the framework, along with code listings exemplifying their usage.
Revised:  We provide a concise mathematical background for the various tools and constructs available in the framework, along with code listings exemplifying their usage.
Edit intent: fluency
Original:  We show how stochastic programming models can be efficiently formulated using expressive syntax .
Revised:  Stochastic programming models can be efficiently formulated using expressive syntax .
Edit intent: coherence
Original:  The framework was implemented to scale seamlessly to distributed environments.
Revised:  The framework scales seamlessly to distributed environments.
Edit intent: clarity
Original:  As a result, stochastic programs are efficiently memory-distributed on supercomputers or cloud architectures and solved using parallel optimization algorithms.
Revised:  Small instances of a model can be run locally to ensure correctness, while larger instances are automatically distributed in a memory-efficient way onto supercomputers or clouds and solved using parallel optimization algorithms.
Edit intent: clarity
Original: A conjecture of Jozsa  states that any polynomial-time quantum computation can be simulated by polynomial-depth classical computation interleaved with logarithmic-depth quantum computation.
Revised: A conjecture of Jozsa states that any polynomial-time quantum computation can be simulated by polylogarithmic-depth quantum computation interleaved with logarithmic-depth quantum computation.
Edit intent: clarity
Original:  As a counterpoint we show that the Welded Tree Problem, which is an oracle problem that can be solved in quantum polynomial time as shown by Childs et al.  , cannot be solved in the class which Jozsa describes.  and \text{JC} whose languages are decided by two different families of interleaved quantum-classical circuits.
Revised:  In this work we show that the Welded Tree Problem, which is an oracle problem that can be solved in quantum polynomial time as shown by Childs et al. , cannot be solved in the class which Jozsa describes. and \text{JC} whose languages are decided by two different families of interleaved quantum-classical circuits.
Edit intent: clarity
Original:  } Therefore, even when interleaved with arbitrary polynomial-time classical computation, greater " Quantum Depth " leads to strictly greater computational ability in this relativized setting.
Revised:  } Therefore, even when interleaved with arbitrary polynomial-time classical computation, greater " quantum depth " leads to strictly greater computational ability in this relativized setting.
Edit intent: fluency
Original:  Separately, Aaronson Aaronson05, Aaronson11, Aaronson14 conjectured that there exists an oracle O such that \text{BQP ^{O} \neq ( \text{BPP )^{O}.
Revised:  Separately, Aaronson Aaronson05, Aaronson11, Aaronson14 conjectured that there exists an oracle O such that BQP ^{O} \neq ( \text{BPP )^{O}.
Edit intent: fluency
Original:  Separately, Aaronson Aaronson05, Aaronson11, Aaronson14 conjectured that there exists an oracle O such that \text{BQP ^{O} \neq ( \text{BPP )^{O}.
Revised:  Separately, Aaronson Aaronson05, Aaronson11, Aaronson14 conjectured that there exists an oracle O such that \text{BQP ^{O} \neq ( BPP )^{O}.
Edit intent: fluency
Original:  ChildsCDFGS03 , cannot be solved in \text{BPP ^{ \text{BQNC \textrm{ }, nor can it be solved in the class that Jozsa describes.
Revised:  ChildsCDFGS03 , cannot be solved in BPP ^{ \text{BQNC \textrm{ }, nor can it be solved in the class that Jozsa describes.
Edit intent: fluency
Original:  More precisely, we define two complexity classes, \text{HQC and \text{JC} } \textrm{ \textrm{ whose languages are decided by two different families of interleaved quantum-classical circuits.
Revised:  More precisely, we define two complexity classes, and \text{JC} } \textrm{ \textrm{ whose languages are decided by two different families of interleaved quantum-classical circuits.
Edit intent: coherence
Original:  More precisely, we define two complexity classes, \text{HQC and \text{JC} } \textrm{ \textrm{ whose languages are decided by two different families of interleaved quantum-classical circuits.
Revised:  More precisely, we define two complexity classes, \text{HQC and \text{JC} } \textrm{HQC \textrm{ whose languages are decided by two different families of interleaved quantum-classical circuits.
Edit intent: fluency
Original:  More precisely, we define two complexity classes, \text{HQC and \text{JC} } \textrm{ \textrm{ whose languages are decided by two different families of interleaved quantum-classical circuits.
Revised:  More precisely, we define two complexity classes, \text{HQC and \text{JC} } \textrm{ \textrm{JC whose languages are decided by two different families of interleaved quantum-classical circuits.
Edit intent: fluency
Original:  \text{HQC contains \text{BPP}^\text{BQNC} } \textrm{ \textrm{  and is therefore relevant to Aaronson's conjecture, while \text{JC \textrm{ captures the model of computation that Jozsa considers.
Revised:  contains \text{BPP}^\text{BQNC} } \textrm{ \textrm{ and is therefore relevant to Aaronson's conjecture, while \text{JC \textrm{ captures the model of computation that Jozsa considers.
Edit intent: coherence
Original:  \text{HQC contains \text{BPP}^\text{BQNC} } \textrm{ \textrm{  and is therefore relevant to Aaronson's conjecture, while \text{JC \textrm{ captures the model of computation that Jozsa considers.
Revised:  \text{HQC contains \text{BPP}^\text{BQNC} } \textrm{HQC \textrm{ and is therefore relevant to Aaronson's conjecture, while \text{JC \textrm{ captures the model of computation that Jozsa considers.
Edit intent: fluency
Original:  \text{HQC contains \text{BPP}^\text{BQNC} } \textrm{ \textrm{  and is therefore relevant to Aaronson's conjecture, while \text{JC \textrm{ captures the model of computation that Jozsa considers.
Revised:  \text{HQC contains \text{BPP}^\text{BQNC} } \textrm{ contains\textrm{ and is therefore relevant to Aaronson's conjecture, while \text{JC \textrm{ captures the model of computation that Jozsa considers.
Edit intent: fluency
Original:  \text{HQC contains \text{BPP}^\text{BQNC} } \textrm{ \textrm{  and is therefore relevant to Aaronson's conjecture, while \text{JC \textrm{ captures the model of computation that Jozsa considers.
Revised:  \text{HQC contains \text{BPP}^\text{BQNC} } \textrm{ \textrm{ and is therefore relevant to Aaronson's conjecture, while \textrm{ captures the model of computation that Jozsa considers.
Edit intent: coherence
Original:  \text{HQC contains \text{BPP}^\text{BQNC} } \textrm{ \textrm{  and is therefore relevant to Aaronson's conjecture, while \text{JC \textrm{ captures the model of computation that Jozsa considers.
Revised:  \text{HQC contains \text{BPP}^\text{BQNC} } \textrm{ \textrm{ and is therefore relevant to Aaronson's conjecture, while \text{JC \textrm{JC captures the model of computation that Jozsa considers.
Edit intent: fluency
Original:  We show that the Welded Tree Problem gives an oracle separation between either of \{ \text{JC, \text{HQC}\} and \text{BQP}} \textrm{ \textrm{ \textrm{ .
Revised:  We show that the Welded Tree Problem gives an oracle separation between either of \{ \text{JC, \text{HQC}\} and \text{BQP}} \textrm{JC \textrm{ \textrm{ .
Edit intent: fluency
Original:  We show that the Welded Tree Problem gives an oracle separation between either of \{ \text{JC, \text{HQC}\} and \text{BQP}} \textrm{ \textrm{ \textrm{ .
Revised:  We show that the Welded Tree Problem gives an oracle separation between either of \{ \text{JC, \text{HQC}\} and \text{BQP}} \textrm{ ,\textrm{ \textrm{ .
Edit intent: fluency
Original:  We show that the Welded Tree Problem gives an oracle separation between either of \{ \text{JC, \text{HQC}\} and \text{BQP}} \textrm{ \textrm{ \textrm{ .
Revised:  We show that the Welded Tree Problem gives an oracle separation between either of \{ \text{JC, \text{HQC}\} and \text{BQP}} \textrm{ \textrm{HQC \textrm{ .
Edit intent: fluency
Original:  We show that the Welded Tree Problem gives an oracle separation between either of \{ \text{JC, \text{HQC}\} and \text{BQP}} \textrm{ \textrm{ \textrm{ .
Revised:  We show that the Welded Tree Problem gives an oracle separation between either of \{ \text{JC, \text{HQC}\} and \text{BQP}} \textrm{ \textrm{ \} and\textrm{ .
Edit intent: fluency
Original:  We show that the Welded Tree Problem gives an oracle separation between either of \{ \text{JC, \text{HQC}\} and \text{BQP}} \textrm{ \textrm{ \textrm{ .
Revised:  We show that the Welded Tree Problem gives an oracle separation between either of \{ \text{JC, \text{HQC}\} and \text{BQP}} \textrm{ \textrm{ \textrm{BQP .
Edit intent: fluency
Original:  To fulfill the lack of information on the interface when the surface current and charge density are unknown, we propose the use of fictitious interface conditions .
Revised:  To fulfill the lack of information , namely the surface current and charge density are unknown, we propose the use of fictitious interface conditions .
Edit intent: clarity
Original:  Numerical experiments in 2-D have shown that CFM-FDTD schemes can achieve high-order convergence, that is third and fourth order convergence in respectively L^{\infty various geometries of the interface.
Revised:  Numerical experiments in 2-D for various geometries of the interface.
Edit intent: clarity
Original:  Given an input, the output of a decision list is the value corresponding to the first rule whole term is satisfied by the input.
Revised:  Given an input, the output of a decision list is the value corresponding to the first rule whose term is satisfied by the input.
Edit intent: clarity
Original:  We prove that decision lists of small width can always be approximated by decision lists of small size, where we obtain sharp bounds (up to constants) .
Revised:  We prove that decision lists of small width can always be approximated by decision lists of small size, where we obtain sharp bounds .
Edit intent: clarity
Original:  For any desired \varepsilon > 0, we construct a family of binary codes of positive rate which can be efficiently list-decoded from any combination of \gamma fraction of insertions and \delta fraction of deletions as long as \gamma+2\delta\leq 1- \varepsilon .
Revised:  For any desired \epsilon > 0, we construct a family of binary codes of positive rate which can be efficiently list-decoded from any combination of \gamma fraction of insertions and \delta fraction of deletions as long as \gamma+2\delta\leq 1- \varepsilon .
Edit intent: clarity