wanyu/IteraTeR_full_sent huggingface dataset:
Original:  (b) algorithms to check whether a module induced in homology by a bifiltration is rectangle-decomposable, and to decompose it in the affirmative, with a better complexity than state-of-the-art decomposition methods for general 2-parameter persistence modules.
Revised:  on the other hand, algorithms to check whether a module induced in homology by a bifiltration is rectangle-decomposable, and to decompose it in the affirmative, with a better complexity than state-of-the-art decomposition methods for general 2-parameter persistence modules.
Edit intent: coherence
Original:  It also admits an algebraic formulation that turns out to be a weaker version of the one for block-decomposability  .
Revised:  It also admits an algebraic formulation that turns out to be a weaker version of the one for block-decomposability . By contrast, we show that general interval-decomposability does not admit such a local characterization, even when locality is understood in a broad sense .
Edit intent: meaning-changed
Original:  The model is trained on the raw waveform to jointly perform the two tasks . Our model infers a set of speaker representations through clustering, which addresses the fundamental permutation problem of speech separation.
Revised:  The model is trained on the raw waveform to jointly perform both tasks from the raw waveform. Wavesplit infers a set of speaker representations through clustering, which addresses the fundamental permutation problem of speech separation.
Edit intent: meaning-changed
Original:  Our model infers a set of speaker representations through clustering, which addresses the fundamental permutation problem of speech separation. Moreover, the sequence-wide speaker representations provide a more robust separation of long, challenging sequences, compared to previous approaches.
Revised:  Our model infers a set of speaker representations through clustering, which addresses the fundamental permutation problem of separation. For speech separation, our sequence-wide speaker representations provide a more robust separation of long, challenging sequences, compared to previous approaches.
Edit intent: coherence
Original:  Moreover, the sequence-wide speaker representations provide a more robust separation of long, challenging sequences, compared to previous approaches. We show that Wavesplit outperforms the previous state-of-the-art on clean mixtures of 2 or 3 speakers ( WSJ0-2mix, WSJ0-3mix ), as well as in noisy (WHAM!) and reverberated (WHAMR!)conditions.
Revised:  Moreover, the sequence-wide speaker representations provide a more robust separation of long, challenging recordings compared to prior work. Wavesplit redefines the state-of-the-art on clean mixtures of 2 or 3 speakers ( WSJ0-2mix, WSJ0-3mix ), as well as in noisy (WHAM!) and reverberated (WHAMR!)conditions.
Edit intent: clarity
Original:  We show that Wavesplit outperforms the previous state-of-the-art on clean mixtures of 2 or 3 speakers ( WSJ0-2mix, WSJ0-3mix ), as well as in noisy (WHAM!) and reverberated (WHAMR!)conditions.
Revised:  We show that Wavesplit outperforms the previous state-of-the-art on clean mixtures of 2 or 3 speakers ( WSJ0-2/3mix ), as well as in noisy (WHAM!) and reverberated (WHAMR!)conditions.
Edit intent: clarity
Original:  We show that Wavesplit outperforms the previous state-of-the-art on clean mixtures of 2 or 3 speakers ( WSJ0-2mix, WSJ0-3mix ), as well as in noisy (WHAM!) and reverberated (WHAMR!)conditions. As an additional contribution, we further improve our model by introducing online data augmentation for separation .
Revised:  We show that Wavesplit outperforms the previous state-of-the-art on clean mixtures of 2 or 3 speakers ( WSJ0-2mix, WSJ0-3mix ), as well as in noisy and reverberated settings (WHAM/WHAMR). We also set a new benchmark on the recent LibriMix dataset. Finally, we show that Wavesplit is also applicable to other domains, by separating fetal and maternal heart rates from a single abdominal electrocardiogram .
Edit intent: meaning-changed
Original: We use the recording queries technique of Zhandry [ Zha19 ] to prove lower bounds in the exponentially small success probability regime, with applications to time-space tradeoffs. We first extend the recording technique to the case of non-uniform input distributions and we describe a new simple framework for using it. Then, as an application, we prove strong direct product theorems for K-Search under a natural product distribution not considered in previous works, and for finding K distinct collisions in a uniform random function ]  . Finally, we use the latter result to obtain the first quantum time-space tradeoff that is not based on a reduction to K-Search.
Revised: We use the recording queries technique of Zhandry [ Zha19 ] \rightarrow ] . Finally, we use the latter result to obtain the first quantum time-space tradeoff that is not based on a reduction to K-Search.
Edit intent: meaning-changed
Original:  Then, as an application, we prove strong direct product theorems for K-Search under a natural product distribution not considered in previous works, and for finding K distinct collisions in a uniform random function ]  . Finally, we use the latter result to obtain the first quantum time-space tradeoff that is not based on a reduction to K-Search.
Revised:  Then, as an application, we prove strong direct product theorems for K-Search under a natural product distribution not considered in previous works, and for finding K distinct collisions in a uniform random function N] . Finally, we use the latter result to obtain the first quantum time-space tradeoff that is not based on a reduction to K-Search.
Edit intent: meaning-changed
Original:  Then, as an application, we prove strong direct product theorems for K-Search under a natural product distribution not considered in previous works, and for finding K distinct collisions in a uniform random function ]  . Finally, we use the latter result to obtain the first quantum time-space tradeoff that is not based on a reduction to K-Search.
Revised:  Then, as an application, we prove strong direct product theorems for K-Search under a natural product distribution not considered in previous works, and for finding K distinct collisions in a uniform random function ] by using a quantum computer. We prove that the number of queries to the function in the quantum random oracle model must increase significantly when the size of the available memory is limited . Finally, we use the latter result to obtain the first quantum time-space tradeoff that is not based on a reduction to K-Search.
Edit intent: meaning-changed
Original:  Then, as an application, we prove strong direct product theorems for K-Search under a natural product distribution not considered in previous works, and for finding K distinct collisions in a uniform random function ]  . Finally, we use the latter result to obtain the first quantum time-space tradeoff that is not based on a reduction to K-Search.
Revised:  Then, as an application, we prove strong direct product theorems for K-Search under a natural product distribution not considered in previous works, and for finding K distinct collisions in a uniform random function ] . 
Edit intent: coherence
Original:  Namely, we demonstrate that any T-query algorithm using S qubits of memory must satisfy a tradeoff of T^3 S \geq \Omega( N^4)for finding \Theta(N) collisions in a random function.
Revised:  Namely, we demonstrate that any algorithm using S qubits of memory must satisfy a tradeoff of T^3 S \geq \Omega( N^4)for finding \Theta(N) collisions in a random function.
Edit intent: clarity
Original:  Namely, we demonstrate that any T-query algorithm using S qubits of memory must satisfy a tradeoff of T^3 S \geq \Omega( N^4)for finding \Theta(N) collisions in a random function.
Revised:  Namely, we demonstrate that any T-query algorithm using S qubits of memory must perform a number T of queries that satisfies the tradeoff T^3 S \geq \Omega( N^4)for finding \Theta(N) collisions in a random function.
Edit intent: clarity
Original:  Namely, we demonstrate that any T-query algorithm using S qubits of memory must satisfy a tradeoff of T^3 S \geq \Omega( N^4)for finding \Theta(N) collisions in a random function. We conjecture that this result can be improved to ] T^2 S \geq \Omega(N^3), and we show that it would imply a T^2 S \geq%DIFDELCMD < \tilde{\Omega}%%% (N^2) tradeoff for Element Distinctness ]  .
Revised:  Namely, we demonstrate that any T-query algorithm using S qubits of memory must satisfy a tradeoff of T^3 S \geq \Omega( K^3 N). Classically, the same question has only been settled recently by Dinur ] T^2 S \geq \Omega(N^3), and we show that it would imply a T^2 S \geq%DIFDELCMD < \tilde{\Omega}%%% (N^2) tradeoff for Element Distinctness ] .
Edit intent: meaning-changed
Original:  We conjecture that this result can be improved to ] T^2 S \geq \Omega(N^3), and we show that it would imply a T^2 S \geq%DIFDELCMD < \tilde{\Omega}%%% (N^2) tradeoff for Element Distinctness ]  .
Revised:  We conjecture that this result can be improved to Eurocrypt'20] T^2 S \geq \Omega(N^3), and we show that it would imply a T^2 S \geq%DIFDELCMD < \tilde{\Omega}%%% (N^2) tradeoff for Element Distinctness ] .
Edit intent: meaning-changed
Original:  We conjecture that this result can be improved to ] T^2 S \geq \Omega(N^3), and we show that it would imply a T^2 S \geq%DIFDELCMD < \tilde{\Omega}%%% (N^2) tradeoff for Element Distinctness ]  .
Revised:  We conjecture that this result can be improved to ], who showed that the Parallel Collision Search algorithm of van Oorschot and Wiener achieves the optimal time-space tradeoff of T^2 S \geq \Omega(N^3), and we show that it would imply a T^2 S \geq%DIFDELCMD < \tilde{\Omega}%%% (N^2) tradeoff for Element Distinctness ] .
Edit intent: meaning-changed
Original:  We conjecture that this result can be improved to ] T^2 S \geq \Omega(N^3), and we show that it would imply a T^2 S \geq%DIFDELCMD < \tilde{\Omega}%%% (N^2) tradeoff for Element Distinctness ]  .
Revised:  We conjecture that this result can be improved to ] T^2 S = \Theta(K^2 N). Our result limits the extent to which quantum computing may decrease this tradeoff. We further show that any improvement to our lower bound would imply a T^2 S \geq%DIFDELCMD < \tilde{\Omega}%%% (N^2) tradeoff for Element Distinctness ] .
Edit intent: meaning-changed
Original:  We conjecture that this result can be improved to ] T^2 S \geq \Omega(N^3), and we show that it would imply a T^2 S \geq%DIFDELCMD < \tilde{\Omega}%%% (N^2) tradeoff for Element Distinctness ]  .
Revised:  We conjecture that this result can be improved to ] T^2 S \geq \Omega(N^3), and we show that it would imply a %DIFDELCMD < \tilde{\Omega}%%% (N^2) tradeoff for Element Distinctness ] .
Edit intent: fluency
Original:  We conjecture that this result can be improved to ] T^2 S \geq \Omega(N^3), and we show that it would imply a T^2 S \geq%DIFDELCMD < \tilde{\Omega}%%% (N^2) tradeoff for Element Distinctness ]  .
Revised:  We conjecture that this result can be improved to ] T^2 S \geq \Omega(N^3), and we show that it would imply a T^2 S \geq%DIFDELCMD < \tilde{\Omega}%%% breakthrough for a related question about the Element Distinctness problem. Our method is based on a novel application of Zhandry's recording query technique ] .
Edit intent: meaning-changed
Original:  We conjecture that this result can be improved to ] T^2 S \geq \Omega(N^3), and we show that it would imply a T^2 S \geq%DIFDELCMD < \tilde{\Omega}%%% (N^2) tradeoff for Element Distinctness ]  .
Revised:  We conjecture that this result can be improved to ] T^2 S \geq \Omega(N^3), and we show that it would imply a T^2 S \geq%DIFDELCMD < \tilde{\Omega}%%% (N^2) tradeoff for Element Distinctness Crypto'19] .
Edit intent: meaning-changed
Original:  We conjecture that this result can be improved to ] T^2 S \geq \Omega(N^3), and we show that it would imply a T^2 S \geq%DIFDELCMD < \tilde{\Omega}%%% (N^2) tradeoff for Element Distinctness ]  .
Revised:  We conjecture that this result can be improved to ] T^2 S \geq \Omega(N^3), and we show that it would imply a T^2 S \geq%DIFDELCMD < \tilde{\Omega}%%% (N^2) tradeoff for Element Distinctness ] for proving lower bounds in the exponentially small success probability regime .
Edit intent: meaning-changed
Original: We unify and extend previous kernelization techniques in sparse classes [ 5,16 ] by defining a structure we call water lilies and show how it can be used in bounded expansion classes to construct linear bikernels for (r, c) -DOMINATING SET , (r, c) -SCATTERED SET, TOTAL r-DOMINATION , r-Roman Domination, and a problem we call (r, [{\lambda}, {\mu}]) -DOMINATION (implying a bikernel for r-PERFECT CODE ).
Revised: We unify and extend previous kernelization techniques in sparse classes [ 6,17 ] by defining a structure we call water lilies and show how it can be used in bounded expansion classes to construct linear bikernels for (r, c) -DOMINATING SET , (r, c) -SCATTERED SET, TOTAL r-DOMINATION , r-Roman Domination, and a problem we call (r, [{\lambda}, {\mu}]) -DOMINATION (implying a bikernel for r-PERFECT CODE ).
Edit intent: meaning-changed
Original: We unify and extend previous kernelization techniques in sparse classes [ 5,16 ] by defining a structure we call water lilies and show how it can be used in bounded expansion classes to construct linear bikernels for (r, c) -DOMINATING SET , (r, c) -SCATTERED SET, TOTAL r-DOMINATION , r-Roman Domination, and a problem we call (r, [{\lambda}, {\mu}]) -DOMINATION (implying a bikernel for r-PERFECT CODE ).
Revised: We unify and extend previous kernelization techniques in sparse classes [ 5,16 ] by defining water lilies and show how it can be used in bounded expansion classes to construct linear bikernels for (r, c) -DOMINATING SET , (r, c) -SCATTERED SET, TOTAL r-DOMINATION , r-Roman Domination, and a problem we call (r, [{\lambda}, {\mu}]) -DOMINATION (implying a bikernel for r-PERFECT CODE ).
Edit intent: clarity
Original: We unify and extend previous kernelization techniques in sparse classes [ 5,16 ] by defining a structure we call water lilies and show how it can be used in bounded expansion classes to construct linear bikernels for (r, c) -DOMINATING SET , (r, c) -SCATTERED SET, TOTAL r-DOMINATION , r-Roman Domination, and a problem we call (r, [{\lambda}, {\mu}]) -DOMINATION (implying a bikernel for r-PERFECT CODE ).
Revised: We unify and extend previous kernelization techniques in sparse classes [ 5,16 ] by defining a structure we call water lilies and show how they can be used in bounded expansion classes to construct linear bikernels for (r, c) -DOMINATING SET , (r, c) -SCATTERED SET, TOTAL r-DOMINATION , r-Roman Domination, and a problem we call (r, [{\lambda}, {\mu}]) -DOMINATION (implying a bikernel for r-PERFECT CODE ).
Edit intent: clarity
Original: We unify and extend previous kernelization techniques in sparse classes [ 5,16 ] by defining a structure we call water lilies and show how it can be used in bounded expansion classes to construct linear bikernels for (r, c) -DOMINATING SET , (r, c) -SCATTERED SET, TOTAL r-DOMINATION , r-Roman Domination, and a problem we call (r, [{\lambda}, {\mu}]) -DOMINATION (implying a bikernel for r-PERFECT CODE ).
Revised: We unify and extend previous kernelization techniques in sparse classes [ 5,16 ] by defining a structure we call water lilies and show how it can be used in bounded expansion classes to construct linear bikernels for (r, c) -Dominating Set , (r, c) -SCATTERED SET, TOTAL r-DOMINATION , r-Roman Domination, and a problem we call (r, [{\lambda}, {\mu}]) -DOMINATION (implying a bikernel for r-PERFECT CODE ).
Edit intent: fluency
Original: We unify and extend previous kernelization techniques in sparse classes [ 5,16 ] by defining a structure we call water lilies and show how it can be used in bounded expansion classes to construct linear bikernels for (r, c) -DOMINATING SET , (r, c) -SCATTERED SET, TOTAL r-DOMINATION , r-Roman Domination, and a problem we call (r, [{\lambda}, {\mu}]) -DOMINATION (implying a bikernel for r-PERFECT CODE ).
Revised: We unify and extend previous kernelization techniques in sparse classes [ 5,16 ] by defining a structure we call water lilies and show how it can be used in bounded expansion classes to construct linear bikernels for (r, c) -DOMINATING SET , (r, c) -Scattered Set, Total r-Domination , r-Roman Domination, and a problem we call (r, [{\lambda}, {\mu}]) -DOMINATION (implying a bikernel for r-PERFECT CODE ).
Edit intent: fluency
Original: We unify and extend previous kernelization techniques in sparse classes [ 5,16 ] by defining a structure we call water lilies and show how it can be used in bounded expansion classes to construct linear bikernels for (r, c) -DOMINATING SET , (r, c) -SCATTERED SET, TOTAL r-DOMINATION , r-Roman Domination, and a problem we call (r, [{\lambda}, {\mu}]) -DOMINATION (implying a bikernel for r-PERFECT CODE ).
Revised: We unify and extend previous kernelization techniques in sparse classes [ 5,16 ] by defining a structure we call water lilies and show how it can be used in bounded expansion classes to construct linear bikernels for (r, c) -DOMINATING SET , (r, c) -SCATTERED SET, TOTAL r-DOMINATION , r-Roman Domination, and a problem we call (r, [{\lambda}, {\mu}]) -Domination (implying a bikernel for r-PERFECT CODE ).
Edit intent: fluency
Original: We unify and extend previous kernelization techniques in sparse classes [ 5,16 ] by defining a structure we call water lilies and show how it can be used in bounded expansion classes to construct linear bikernels for (r, c) -DOMINATING SET , (r, c) -SCATTERED SET, TOTAL r-DOMINATION , r-Roman Domination, and a problem we call (r, [{\lambda}, {\mu}]) -DOMINATION (implying a bikernel for r-PERFECT CODE ).
Revised: We unify and extend previous kernelization techniques in sparse classes [ 5,16 ] by defining a structure we call water lilies and show how it can be used in bounded expansion classes to construct linear bikernels for (r, c) -DOMINATING SET , (r, c) -SCATTERED SET, TOTAL r-DOMINATION , r-Roman Domination, and a problem we call (r, [{\lambda}, {\mu}]) -DOMINATION (implying a bikernel for r-Perfect Code ).
Edit intent: fluency
Original:  At the cost of slightly changing the output graph class these bikernels can be turned into into kernels. Finally, we demonstrate how these constructions can be combined to create 'multikernels', meaning graphs who represent kernels for multiple problems at once.
Revised:  At the cost of slightly changing the output graph class these bikernels can be turned into kernels. We further demonstrate how these constructions can be combined to create 'multikernels', meaning graphs who represent kernels for multiple problems at once.
Edit intent: clarity
Original: We introduce a decision-making model based on value functions that include individualistic utility function and socio-constructivistic norm function , and propose a norm-fostering process that recursively updates norm function through mutual recognition between the self and others.
Revised: We introduced a decision-making model based on value functions that include individualistic utility function and socio-constructivistic norm function , and propose a norm-fostering process that recursively updates norm function through mutual recognition between the self and others.
Edit intent: fluency
Original: We introduce a decision-making model based on value functions that include individualistic utility function and socio-constructivistic norm function , and propose a norm-fostering process that recursively updates norm function through mutual recognition between the self and others.
Revised: We introduce a decision-making model based on value functions that included individualistic utility function and socio-constructivistic norm function , and propose a norm-fostering process that recursively updates norm function through mutual recognition between the self and others.
Edit intent: fluency
Original: We introduce a decision-making model based on value functions that include individualistic utility function and socio-constructivistic norm function , and propose a norm-fostering process that recursively updates norm function through mutual recognition between the self and others.
Revised: We introduce a decision-making model based on value functions that include individualistic utility function and socio-constructivistic norm function and proposed a norm-fostering process that recursively updates norm function through mutual recognition between the self and others.
Edit intent: fluency
Original:  As an example, we will look at the resource-sharing problem typical of economic activities and assume the distribution of individual actions to define the (1) norm function fostered through mutual comparison of value/action ratio based on the equity theory (progressive tax-like), (2) norm function proportional to resource utilization (proportional tax-like) and (3) fixed norm function independent of resource utilization (fixed tax-like).
Revised:  As an example, we looked at the resource-sharing problem typical of economic activities and assume the distribution of individual actions to define the (1) norm function fostered through mutual comparison of value/action ratio based on the equity theory (progressive tax-like), (2) norm function proportional to resource utilization (proportional tax-like) and (3) fixed norm function independent of resource utilization (fixed tax-like).
Edit intent: coherence
Original:  As an example, we will look at the resource-sharing problem typical of economic activities and assume the distribution of individual actions to define the (1) norm function fostered through mutual comparison of value/action ratio based on the equity theory (progressive tax-like), (2) norm function proportional to resource utilization (proportional tax-like) and (3) fixed norm function independent of resource utilization (fixed tax-like).
Revised:  As an example, we will look at the resource-sharing problem typical of economic activities and assumed the distribution of individual actions to define the (1) norm function fostered through mutual comparison of value/action ratio based on the equity theory (progressive tax-like), (2) norm function proportional to resource utilization (proportional tax-like) and (3) fixed norm function independent of resource utilization (fixed tax-like).
Edit intent: fluency
Original:  And, by carrying out numerical simulation, we will show that the progressive tax-like norm function (i) does not increase disparity for the distribution of the actions, unlike the other norm functions, and (ii) has high resource productivity and low Gini coefficient , i. e., the progressive tax-like norm function has the highest sustainability and fairness.
Revised:  By carrying out numerical simulation, we will show that the progressive tax-like norm function (i) does not increase disparity for the distribution of the actions, unlike the other norm functions, and (ii) has high resource productivity and low Gini coefficient , i. e., the progressive tax-like norm function has the highest sustainability and fairness.
Edit intent: coherence
Original:  And, by carrying out numerical simulation, we will show that the progressive tax-like norm function (i) does not increase disparity for the distribution of the actions, unlike the other norm functions, and (ii) has high resource productivity and low Gini coefficient , i. e., the progressive tax-like norm function has the highest sustainability and fairness.
Revised:  And, by carrying out numerical simulation, we showed that the progressive tax-like norm function (i) does not increase disparity for the distribution of the actions, unlike the other norm functions, and (ii) has high resource productivity and low Gini coefficient , i. e., the progressive tax-like norm function has the highest sustainability and fairness.
Edit intent: coherence