wanyu/IteraTeR_v2 huggingface dataset:
Original:  We show that such restricted%DIFDELCMD < {\rm %%% postBQP classes are in%DIFDELCMD < {\rm %DIFDELCMD < %%% AWPP (\subseteq{\rm PP=}%DIFDELCMD < {\rm %%% postBQP ).
Revised:  We show that such restricted%DIFDELCMD < {\rm %%% postBQP classes are in%DIFDELCMD < {\rm %DIFDELCMD < %%% (\subseteq{\rm PP=}%DIFDELCMD < {\rm %%% postBQP ).
Edit intent: clarity
Original:  We show that such restricted%DIFDELCMD < {\rm %%% postBQP classes are in%DIFDELCMD < {\rm %DIFDELCMD < %%% AWPP (\subseteq{\rm PP=}%DIFDELCMD < {\rm %%% postBQP ).
Revised:  We show that such restricted%DIFDELCMD < {\rm %%% postBQP classes are in%DIFDELCMD < {\rm %DIFDELCMD < %%% AWPP (\subseteq{\rm PP=}%DIFDELCMD < {\rm %%% ).
Edit intent: fluency
Original:  This result suggests that postselecting an event with an exponentially small probability does not necessarily boost%DIFDELCMD < {\rm %%% BQP to PP.
Revised:  This result suggests that postselecting an event with an exponentially small probability does not necessarily boost%DIFDELCMD < {\rm %%% to PP.
Edit intent: clarity
Original:  The best upperbound of %DIFDELCMD < {\rm %%% BQP is %DIFDELCMD < {\rm %%% AWPP , and therefore restricted%DIFDELCMD < {\rm %%% postBQP classes are other examples of complexity classes " slightly above {\rm BQP } ".
Revised:  The best upperbound of %DIFDELCMD < {\rm %%% BQP is %DIFDELCMD < {\rm %%% , and therefore restricted%DIFDELCMD < {\rm %%% postBQP classes are other examples of complexity classes " slightly above {\rm BQP } ".
Edit intent: clarity
Original:  The best upperbound of %DIFDELCMD < {\rm %%% BQP is %DIFDELCMD < {\rm %%% AWPP , and therefore restricted%DIFDELCMD < {\rm %%% postBQP classes are other examples of complexity classes " slightly above {\rm BQP } ".
Revised:  The best upperbound of %DIFDELCMD < {\rm %%% BQP is %DIFDELCMD < {\rm %%% AWPP %DIFDELCMD < {\rm %%% postBQP classes are other examples of complexity classes " slightly above {\rm BQP } ".
Edit intent: coherence
Original:  The best upperbound of %DIFDELCMD < {\rm %%% BQP is %DIFDELCMD < {\rm %%% AWPP , and therefore restricted%DIFDELCMD < {\rm %%% postBQP classes are other examples of complexity classes " slightly above {\rm BQP } ".
Revised:  The best upperbound of %DIFDELCMD < {\rm %%% BQP is %DIFDELCMD < {\rm %%% AWPP , and therefore restricted%DIFDELCMD < {\rm %%% classes are other examples of complexity classes " slightly above {\rm BQP } ".
Edit intent: fluency
Original:  The best upperbound of %DIFDELCMD < {\rm %%% BQP is %DIFDELCMD < {\rm %%% AWPP , and therefore restricted%DIFDELCMD < {\rm %%% postBQP classes are other examples of complexity classes " slightly above {\rm BQP } ".
Revised:  The best upperbound of %DIFDELCMD < {\rm %%% BQP is %DIFDELCMD < {\rm %%% AWPP , and therefore restricted%DIFDELCMD < {\rm %%% postBQP classes are other examples of complexity classes " slightly above {\rm BPP } ".
Edit intent: fluency
Original: capacity of a general probabilistic theory which satisfies the tomographic locality is in {\rm AWPP . Our result therefore implies that quantum physics with restricted postselections is an example of a super quantum theory which seems to be outside of their general probabilistic theory but its computational capacity is also in%DIFDELCMD < {\rm %%% AWPP . Although it is physically natural to expect that such restricted%DIFDELCMD < {\rm %%% postBQP classes are not equivalent to BQP,
Revised: capacity of a general probabilistic theory which satisfies the tomographic locality is in {\rm . Our result therefore implies that quantum physics with restricted postselections is an example of a super quantum theory which seems to be outside of their general probabilistic theory but its computational capacity is also in%DIFDELCMD < {\rm %%% AWPP . Although it is physically natural to expect that such restricted%DIFDELCMD < {\rm %%% postBQP classes are not equivalent to BQP,
Edit intent: fluency
Original: capacity of a general probabilistic theory which satisfies the tomographic locality is in {\rm AWPP . Our result therefore implies that quantum physics with restricted postselections is an example of a super quantum theory which seems to be outside of their general probabilistic theory but its computational capacity is also in%DIFDELCMD < {\rm %%% AWPP . Although it is physically natural to expect that such restricted%DIFDELCMD < {\rm %%% postBQP classes are not equivalent to BQP,
Revised: capacity of a general probabilistic theory which satisfies the tomographic locality is in {\rm AWPP %DIFDELCMD < {\rm %%% AWPP . Although it is physically natural to expect that such restricted%DIFDELCMD < {\rm %%% postBQP classes are not equivalent to BQP,
Edit intent: coherence
Original: capacity of a general probabilistic theory which satisfies the tomographic locality is in {\rm AWPP . Our result therefore implies that quantum physics with restricted postselections is an example of a super quantum theory which seems to be outside of their general probabilistic theory but its computational capacity is also in%DIFDELCMD < {\rm %%% AWPP . Although it is physically natural to expect that such restricted%DIFDELCMD < {\rm %%% postBQP classes are not equivalent to BQP,
Revised: capacity of a general probabilistic theory which satisfies the tomographic locality is in {\rm AWPP . Our result therefore implies that quantum physics with restricted postselections is an example of a super quantum theory which seems to be outside of their general probabilistic theory but its computational capacity is also in%DIFDELCMD < {\rm %%% . Although it is physically natural to expect that such restricted%DIFDELCMD < {\rm %%% postBQP classes are not equivalent to BQP,
Edit intent: fluency
Original: capacity of a general probabilistic theory which satisfies the tomographic locality is in {\rm AWPP . Our result therefore implies that quantum physics with restricted postselections is an example of a super quantum theory which seems to be outside of their general probabilistic theory but its computational capacity is also in%DIFDELCMD < {\rm %%% AWPP . Although it is physically natural to expect that such restricted%DIFDELCMD < {\rm %%% postBQP classes are not equivalent to BQP,
Revised: capacity of a general probabilistic theory which satisfies the tomographic locality is in {\rm AWPP . Our result therefore implies that quantum physics with restricted postselections is an example of a super quantum theory which seems to be outside of their general probabilistic theory but its computational capacity is also in%DIFDELCMD < {\rm %%% AWPP %DIFDELCMD < {\rm %%% postBQP classes are not equivalent to BQP,
Edit intent: coherence
Original:  we show that%DIFDELCMD < {\rm %%% UP} \cap{\rm coUP, which is unlikely to be in BQP, is contained in the restricted }%DIFDELCMD < {\rm %%% postBQP classes.
Revised:  we show that%DIFDELCMD < {\rm %%% UP} , which is unlikely to be in BQP, is contained in the restricted }%DIFDELCMD < {\rm %%% postBQP classes.
Edit intent: coherence
Original:  we show that%DIFDELCMD < {\rm %%% UP} \cap{\rm coUP, which is unlikely to be in BQP, is contained in the restricted }%DIFDELCMD < {\rm %%% postBQP classes.
Revised:  we show that%DIFDELCMD < {\rm %%% UP} \cap{\rm coUP, which is unlikely to be in BQP, is contained in the restricted }%DIFDELCMD < {\rm %%% classes.
Edit intent: clarity
Original:  Finally, we also consider another restricted class of%DIFDELCMD < {\rm %%% postBQP , where the postselected probability depends only on the size of inputs.
Revised:  Finally, we also consider another restricted class of%DIFDELCMD < {\rm %%% , where the postselected probability depends only on the size of inputs.
Edit intent: clarity
Original:  We show that this restricted version is contained in%DIFDELCMD < {\rm %%% APP , where%DIFDELCMD < {\rm %%% AWPP \subseteq{\rm APP\subseteq{\rm PP}=}%DIFDELCMD < {\rm %DIFDELCMD < %%% postBQP .
Revised:  We show that this restricted version is contained in%DIFDELCMD < {\rm %%% , where%DIFDELCMD < {\rm %%% AWPP \subseteq{\rm APP\subseteq{\rm PP}=}%DIFDELCMD < {\rm %DIFDELCMD < %%% postBQP .
Edit intent: fluency
Original:  We show that this restricted version is contained in%DIFDELCMD < {\rm %%% APP , where%DIFDELCMD < {\rm %%% AWPP \subseteq{\rm APP\subseteq{\rm PP}=}%DIFDELCMD < {\rm %DIFDELCMD < %%% postBQP .
Revised:  We show that this restricted version is contained in%DIFDELCMD < {\rm %%% APP %DIFDELCMD < {\rm %%% AWPP \subseteq{\rm APP\subseteq{\rm PP}=}%DIFDELCMD < {\rm %DIFDELCMD < %%% postBQP .
Edit intent: coherence
Original:  We show that this restricted version is contained in%DIFDELCMD < {\rm %%% APP , where%DIFDELCMD < {\rm %%% AWPP \subseteq{\rm APP\subseteq{\rm PP}=}%DIFDELCMD < {\rm %DIFDELCMD < %%% postBQP .
Revised:  We show that this restricted version is contained in%DIFDELCMD < {\rm %%% APP , where%DIFDELCMD < {\rm %%% AWPP \subseteq{\rm PP}=}%DIFDELCMD < {\rm %DIFDELCMD < %%% postBQP .
Edit intent: fluency
Original: The proliferation of massive datasets combined with the development of sophisticated analytical techniques have enabled a wide variety of novel applications such as improved product recommendations, automatic image tagging, and improved speech driven interfaces.
Revised: The proliferation of massive datasets combined with the development of sophisticated analytical techniques have enabled a wide variety of novel applications such as improved product recommendations, automatic image tagging, and improved speech-driven interfaces.
Edit intent: fluency
Original:  The major obstacle to supporting these queries is the challenging and expensive process of PAQ planning, which involves identifying and training an appropriate predictive model.
Revised:  A major obstacle to supporting these queries is the challenging and expensive process of PAQ planning, which involves identifying and training an appropriate predictive model.
Edit intent: fluency
Original:  The major obstacle to supporting these queries is the challenging and expensive process of PAQ planning, which involves identifying and training an appropriate predictive model.
Revised:  The major obstacle to supporting PAQs is the challenging and expensive process of PAQ planning, which involves identifying and training an appropriate predictive model.
Edit intent: clarity
Original:  The major obstacle to supporting these queries is the challenging and expensive process of PAQ planning, which involves identifying and training an appropriate predictive model.
Revised:  The major obstacle to supporting these queries is the challenging and expensive process of identifying and training an appropriate predictive model.
Edit intent: clarity
Original:  The resulting system, TUPAQ, solves the PAQ planning problem with comparable accuracy to exhaustive strategies but an order of magnitude faster , and can scale to models trained on terabytes of data across hundreds of machines.
Revised:  The resulting system, TUPAQ, solves the PAQ planning problem with comparable quality to exhaustive strategies but an order of magnitude faster , and can scale to models trained on terabytes of data across hundreds of machines.
Edit intent: clarity
Original:  We describe two spectral algorithms for this task based on the non-cktracking and the Bethe Hessian operators.
Revised:  We describe two spectral algorithms for this task based on the non-backtracking and the Bethe Hessian operators.
Edit intent: fluency
Original: This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data applications.
Revised: This paper is concerned with the problem of low-rank plus sparse matrix decomposition for big data applications.
Edit intent: fluency
Original:  second, they are based on an optimization problem whose dimensionality is equal to the dimension of the given data.
Revised:  second, they are based on optimization problems that scale with the dimension of the given data.
Edit intent: clarity
Original:  It is shown that when the columns/rows subspace of the low rank matrix is incoherent with the standard basis, the columns/ rows subspace can be learned from a small random subset of the columns/ rows of the given data matrix.
Revised:  It is shown that when the columns/rows subspace of the low rank matrix is incoherent with the standard basis, the columns/ rows of the given data matrix.
Edit intent: clarity
Original: This paper is concerned with the problem of low-rank plus sparse matrix decomposition for big data.
Revised: This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data.
Edit intent: fluency
Original:  Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on optimization problems that scale with the dimension of the data, which limit their scalability.
Revised:  Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on optimization problems with complexity that scales with the dimension of the data, which limit their scalability.
Edit intent: clarity
Original:  Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on optimization problems that scale with the dimension of the data, which limit their scalability.
Revised:  Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on optimization problems that scale with the dimension of the data, which limits their scalability.
Edit intent: fluency
Original:  Furthermore, the existing randomized approaches mostly rely on uniform random sampling, which can be quite inefficient for many real world data matrices that exhibit additional structures (e.g. clustering).
Revised:  Furthermore, existing randomized approaches mostly rely on uniform random sampling, which can be quite inefficient for many real world data matrices that exhibit additional structures (e.g. clustering).
Edit intent: fluency
Original:  Furthermore, the existing randomized approaches mostly rely on uniform random sampling, which can be quite inefficient for many real world data matrices that exhibit additional structures (e.g. clustering).
Revised:  Furthermore, the existing randomized approaches mostly rely on uniform random sampling, which is quite inefficient for many real world data matrices that exhibit additional structures (e.g. clustering).
Edit intent: coherence
Original:  Even when the data is sampled uniformly at random, it is shown that the sufficient number of sampled columns/rows is roughly O(r\mu), where \mu is the coherency parameter and r the rank of the low-rank component.
Revised:  Even when the data is sampled uniformly at random, it is shown that the sufficient number of sampled columns/rows is roughly O(r\mu), where \mu is the coherency parameter and r the rank of the low rank component.
Edit intent: fluency
Original:  In addition, efficient sampling algorithms are proposed to address the problem of column/row sampling from structured data.
Revised:  In addition, adaptive sampling algorithms are proposed to address the problem of column/row sampling from structured data.
Edit intent: clarity
Original:  The proposed sampling algorithms can be independently used for feature selection from high-dimensional data.
Revised:  We provide an analysis of the proposed method with adaptive sampling and show that adaptive sampling makes the required number of sampled columns/rows invariant to the distribution of the data.
Edit intent: clarity
Original:  This simulation hindcasts the emergence and expansion of agropastoral life style in 294 regions of Eurasia and North Africa.
Revised:  Simulations hindcast the emergence and expansion of agropastoral life style in 294 regions of Eurasia and North Africa.
Edit intent: clarity
Original:  This study shows that there is no simple or exclusive demic or cultural answer , but that in most regions of Eurasia both demic and cultural processes are active, sometimes concurrently, sometimes alternating .
Revised:  This study shows that there is no simple or exclusive demic or cultural diffusion , but that in most regions of Eurasia both demic and cultural processes are active, sometimes concurrently, sometimes alternating .
Edit intent: clarity
Original:  This study shows that there is no simple or exclusive demic or cultural answer , but that in most regions of Eurasia both demic and cultural processes are active, sometimes concurrently, sometimes alternating .
Revised:  This study shows that there is no simple or exclusive demic or cultural answer , but that in most regions of Eurasia a combination of demic and cultural processes are active, sometimes concurrently, sometimes alternating .
Edit intent: clarity
Original:  I argue to investigate diffusion processes in a diachronic fashion and not from a time-integrated perspective : the complexity of diffusion processes that this deterministic model shows should be expected to have been surpassed by past people who made choices and pursued interests .
Revised:  This study affirms that diffusion processes should be investigated in a diachronic fashion and not from a time-integrated perspective : the complexity of diffusion processes that this deterministic model shows should be expected to have been surpassed by past people who made choices and pursued interests .
Edit intent: clarity
Original:  I argue to investigate diffusion processes in a diachronic fashion and not from a time-integrated perspective : the complexity of diffusion processes that this deterministic model shows should be expected to have been surpassed by past people who made choices and pursued interests .
Revised:  I argue to investigate diffusion processes in a diachronic fashion and not from a time-integrated perspective .
Edit intent: clarity
Original:  monotonic increases or decreases of citation intensity (cited or citing) and critical revisions of the a posteriori ( 2013) prediction in 2012 on the basis of 2011 data . Changes can be studied at the level of journals using the margin totals of entropy production along the row or column vectors, but also at the level of links among groups of journals by importing the transition matrices into network analysis and visualization programs (and using community-finding algorithms).
Revised:  monotonic increases or decreases of citation intensity (cited or citing) and critical revisions of the a posteriori ( 2013) are studied using methodologies based on entropy statistics . Changes can be studied at the level of journals using the margin totals of entropy production along the row or column vectors, but also at the level of links among groups of journals by importing the transition matrices into network analysis and visualization programs (and using community-finding algorithms).
Edit intent: clarity
Original:  monotonic increases or decreases of citation intensity (cited or citing) and critical revisions of the a posteriori ( 2013) prediction in 2012 on the basis of 2011 data . Changes can be studied at the level of journals using the margin totals of entropy production along the row or column vectors, but also at the level of links among groups of journals by importing the transition matrices into network analysis and visualization programs (and using community-finding algorithms).
Revised:  monotonic increases or decreases of citation intensity (cited or citing) and critical revisions of the a posteriori ( 2013) prediction in 2012 on the basis of 2011 data . Changes can be indicated at the level of journals using the margin totals of entropy production along the row or column vectors, but also at the level of links among groups of journals by importing the transition matrices into network analysis and visualization programs (and using community-finding algorithms).
Edit intent: clarity
Original:  monotonic increases or decreases of citation intensity (cited or citing) and critical revisions of the a posteriori ( 2013) prediction in 2012 on the basis of 2011 data . Changes can be studied at the level of journals using the margin totals of entropy production along the row or column vectors, but also at the level of links among groups of journals by importing the transition matrices into network analysis and visualization programs (and using community-finding algorithms).
Revised:  monotonic increases or decreases of citation intensity (cited or citing) and critical revisions of the a posteriori ( 2013) prediction in 2012 on the basis of 2011 data . Changes can be studied at the level of journals using the margin totals of entropy production along the row or column vectors, but also at the level of links among journals by importing the transition matrices into network analysis and visualization programs (and using community-finding algorithms).
Edit intent: clarity
Original:  Specifically, it focuses on the deep understanding of the risk in terms of threats, vulnerabilities and consequences that arise from cyber-attacks .
Revised:  It focuses on the deep understanding of the risk in terms of threats, vulnerabilities and consequences that arise from cyber-attacks .
Edit intent: coherence
Original:  In previous work on instruction sequence size complexity, we chose instruction sets for Boolean registers that contain only  a few of the possible instructions .
Revised:  In previous work on instruction sequence size complexity, we chose instruction sets for Boolean registers that contain only instructions of a few of the possible instructions .
Edit intent: clarity
Original:  In previous work on instruction sequence size complexity, we chose instruction sets for Boolean registers that contain only  a few of the possible instructions .
Revised:  In previous work on instruction sequence size complexity, we chose instruction sets for Boolean registers that contain only a few of the possible kinds .
Edit intent: clarity
Original:  This work is among other things a requisite for making progress with proving lower bounds of non-asymptotic instruction sequence size complexity in cases where auxiliary Boolean registers may be used .
Revised:  We expect that the results of this study will turn out to be useful to adequately assess results of work that is concerned with lower bounds of non-asymptotic instruction sequence size complexity in cases where auxiliary Boolean registers may be used .
Edit intent: clarity
Original:  This work is among other things a requisite for making progress with proving lower bounds of non-asymptotic instruction sequence size complexity in cases where auxiliary Boolean registers may be used .
Revised:  This work is among other things a requisite for making progress with proving lower bounds of instruction sequence size complexity in cases where auxiliary Boolean registers may be used .
Edit intent: clarity
Original:  This work is among other things a requisite for making progress with proving lower bounds of non-asymptotic instruction sequence size complexity in cases where auxiliary Boolean registers may be used .
Revised:  This work is among other things a requisite for making progress with proving lower bounds of non-asymptotic instruction sequence size complexity .
Edit intent: clarity
Original:  If f is symmetric, then m\cdot d_{p_1^{e_1}}(f) \cdots d_{p_r^{e_r}}(f) > n. If f is non-symmetric, by the second moment method we prove almost always m\cdot d_{p_1^{e_1}}(f) \cdots d_{p_r^{e_r}}(f) > n-1.
Revised:  If f is symmetric, then m\cdot d_{p_1^{e_1}}(f) ... d_{p_r^{e_r}}(f) > n. If f is non-symmetric, by the second moment method we prove almost always m\cdot d_{p_1^{e_1}}(f) \cdots d_{p_r^{e_r}}(f) > n-1.
Edit intent: coherence
Original:  If f is symmetric, then m\cdot d_{p_1^{e_1}}(f) \cdots d_{p_r^{e_r}}(f) > n. If f is non-symmetric, by the second moment method we prove almost always m\cdot d_{p_1^{e_1}}(f) \cdots d_{p_r^{e_r}}(f) > n-1.
Revised:  If f is symmetric, then m\cdot d_{p_1^{e_1}}(f) \cdots d_{p_r^{e_r}}(f) > n. If f is non-symmetric, by the second moment method we prove almost always m\cdot d_{p_1^{e_1}}(f) ... d_{p_r^{e_r}}(f) > n-1.
Edit intent: coherence