wanyu/IteraTeR_v2 huggingface dataset:
Original:  However, this function might be inefficient because of the following two reasons\emph{  : (a) it involves a lot of computations or (b) a huge amount of auxiliary randomness is required.
Revised:  However, this function might be inefficient because of the following two reasons\emph{ when : (a) it involves a lot of computations or (b) a huge amount of auxiliary randomness is required.
Edit intent: clarity
Original:  In this work we study this problem in the computational setting, where efficiently simulating Z from X becomes possible if we don't require the simulator output to be identical to Z but only computationally indistinguishable .
Revised:  We study this problem in the computational setting, where efficiently simulating Z from X becomes possible if we don't require the simulator output to be identical to Z but only computationally indistinguishable .
Edit intent: clarity
Original:  We prove the following result: for any X\in\{0,1\}^n and any correlated Z\in\{0,1\} ^m, for every choice of parameters (\epsilon,s) there is a randomized function hfrom n to m bits of complexity O(s  2^{ 2m }\epsilon^{-2}) such that Z and h (X) are (\epsilon,s)-indistinguishable given X.
Revised:  We prove the following result: for any X\in\{0,1\}^n , any correlated Z\in\{0,1\} ^m, for every choice of parameters (\epsilon,s) there is a randomized function hfrom n to m bits of complexity O(s 2^{ 2m }\epsilon^{-2}) such that Z and h (X) are (\epsilon,s)-indistinguishable given X.
Edit intent: fluency
Original:  We prove the following result: for any X\in\{0,1\}^n and any correlated Z\in\{0,1\} ^m, for every choice of parameters (\epsilon,s) there is a randomized function hfrom n to m bits of complexity O(s  2^{ 2m }\epsilon^{-2}) such that Z and h (X) are (\epsilon,s)-indistinguishable given X.
Revised:  We prove the following result: for any X\in\{0,1\}^n and any correlated Z\in\{0,1\} ^\ell and every choice of parameters (\epsilon,s) there is a randomized function hfrom n to m bits of complexity O(s 2^{ 2m }\epsilon^{-2}) such that Z and h (X) are (\epsilon,s)-indistinguishable given X.
Edit intent: fluency
Original:  We prove the following result: for any X\in\{0,1\}^n and any correlated Z\in\{0,1\} ^m, for every choice of parameters (\epsilon,s) there is a randomized function hfrom n to m bits of complexity O(s  2^{ 2m }\epsilon^{-2}) such that Z and h (X) are (\epsilon,s)-indistinguishable given X.
Revised:  We prove the following result: for any X\in\{0,1\}^n and any correlated Z\in\{0,1\} ^m, for every choice of (\epsilon,s) there is a randomized function hfrom n to m bits of complexity O(s 2^{ 2m }\epsilon^{-2}) such that Z and h (X) are (\epsilon,s)-indistinguishable given X.
Edit intent: clarity
Original:  We prove the following result: for any X\in\{0,1\}^n and any correlated Z\in\{0,1\} ^m, for every choice of parameters (\epsilon,s) there is a randomized function hfrom n to m bits of complexity O(s  2^{ 2m }\epsilon^{-2}) such that Z and h (X) are (\epsilon,s)-indistinguishable given X.
Revised:  We prove the following result: for any X\in\{0,1\}^n and any correlated Z\in\{0,1\} ^m, for every choice of parameters (\epsilon,s) there is a randomized function hfrom n to m bits of complexity O(s 2^{ 2\ell }\epsilon^{-2}) such that Z and h (X) are (\epsilon,s)-indistinguishable given X.
Edit intent: fluency
Original:  We prove the following result: for any X\in\{0,1\}^n and any correlated Z\in\{0,1\} ^m, for every choice of parameters (\epsilon,s) there is a randomized function hfrom n to m bits of complexity O(s  2^{ 2m }\epsilon^{-2}) such that Z and h (X) are (\epsilon,s)-indistinguishable given X.
Revised:  We prove the following result: for any X\in\{0,1\}^n and any correlated Z\in\{0,1\} ^m, for every choice of parameters (\epsilon,s) there is a randomized function hfrom n to m bits of complexity O(s 2^{ 2m }\epsilon^{-2}) such that Z and h X are (\epsilon,s)-indistinguishable given X.
Edit intent: clarity
Original:  This bound is better than in the original proof of Pietrzak and Jetchev (TCC'14) and (surprisingly!) much better for some practically interesting settings than in the alternative proof due to Vadhan and Zheng (CRYPTO'13).
Revised:  This is better than in the original proof of Pietrzak and Jetchev (TCC'14) and (surprisingly!) much better for some practically interesting settings than in the alternative proof due to Vadhan and Zheng (CRYPTO'13).
Edit intent: clarity
Original:  This bound is better than in the original proof of Pietrzak and Jetchev (TCC'14) and (surprisingly!) much better for some practically interesting settings than in the alternative proof due to Vadhan and Zheng (CRYPTO'13).
Revised:  This bound is better than in the original proof of Pietrzak and Jetchev (TCC'14) and much better for some practically interesting settings than in the alternative proof due to Vadhan and Zheng (CRYPTO'13).
Edit intent: coherence
Original:  This bound is better than in the original proof of Pietrzak and Jetchev (TCC'14) and (surprisingly!) much better for some practically interesting settings than in the alternative proof due to Vadhan and Zheng (CRYPTO'13).
Revised:  This bound is better than in the original proof of Pietrzak and Jetchev (TCC'14) and (surprisingly!) much better for some practically interesting settings than the alternative bound due to Vadhan and Zheng (CRYPTO'13).
Edit intent: fluency
Original:  Our approach is also much simpler and modular (the standard min-max theorem and a L_2-approximation argument).
Revised:  Our approach is also simpler and modular (the standard min-max theorem and a L_2-approximation argument).
Edit intent: clarity
Original:  Our approach is also much simpler and modular (the standard min-max theorem and a L_2-approximation argument).
Revised:  Our approach is also much simpler and modular (the standard min-max theorem combined with an L_2-approximation argument).
Edit intent: clarity
Original:  As a contribution of independent interests, we provide a clear analysis of \\%DIF > . As a contribution of independent interests, we provide a clear analysis  provable security for the (best known ) simulator-based proof technique of this construction , showing how the adversary's time/success ratio depends on the simulator complexity .
Revised:  As a contribution of independent interests, we provide a clear analysis of \\%DIF > . As a contribution of independent interests, we provide a clear analysis of the provable security for the (best known ) simulator-based proof technique of this construction , showing how the adversary's time/success ratio depends on the simulator complexity .
Edit intent: fluency
Original:  As a contribution of independent interests, we provide a clear analysis of \\%DIF > . As a contribution of independent interests, we provide a clear analysis  provable security for the (best known ) simulator-based proof technique of this construction , showing how the adversary's time/success ratio depends on the simulator complexity .
Revised:  As a contribution of independent interests, we provide a clear analysis of \\%DIF > . As a contribution of independent interests, we provide a clear analysis provable security for the best known proof technique of this construction , showing how the adversary's time/success ratio depends on the simulator complexity .
Edit intent: clarity
Original:  As a contribution of independent interests, we provide a clear analysis of \\%DIF > . As a contribution of independent interests, we provide a clear analysis  provable security for the (best known ) simulator-based proof technique of this construction , showing how the adversary's time/success ratio depends on the simulator complexity .
Revised:  As a contribution of independent interests, we provide a clear analysis of \\%DIF > . As a contribution of independent interests, we provide a clear analysis provable security for the (best known ) simulator-based proof technique of this construction .
Edit intent: coherence
Original:  In particular we show that, contrarily to what have been suggested,  AES is not enough for this construction and one needs a weak PRF with 512-bit keys, like SHA512.
Revised:  In particular we show that, contrarily to what have been suggested, AES is not enough for this construction and one needs a weak PRF with 512 bits of security, for example a weak PRF instantiated with SHA512.
Edit intent: clarity
Original:  Interestingly, we discover serious limitations for the powerful Uniform Min-Max Theorem of Vadhan and Zheng: applied for this setting , it does not provide any meaningful security .%DIFDELCMD < \end{abstract} %DIFDELCMD < %%% \\%DIF > higher).
Revised:  Interestingly, we discover limitations for regularity theorems of Vadhan and Zheng: applied for this setting , it does not provide any meaningful security .%DIFDELCMD < \end{abstract} %DIFDELCMD < %%% \\%DIF > higher).
Edit intent: clarity
Original:  Interestingly, we discover serious limitations for the powerful Uniform Min-Max Theorem of Vadhan and Zheng: applied for this setting , it does not provide any meaningful security .%DIFDELCMD < \end{abstract} %DIFDELCMD < %%% \\%DIF > higher).
Revised:  Interestingly, we discover serious limitations for the powerful Uniform Min-Max Theorem of Vadhan and Zheng: %DIFDELCMD < \end{abstract} %DIFDELCMD < %%% \\%DIF > higher).
Edit intent: coherence
Original: Given a distribution X,any correlated information Zcan be represented as a randomized function of X.
Revised: For any pair (X,Z) of correlated random variables we can think of Z as a randomized function of X.
Edit intent: clarity
Original:  However, it might be\emph{extremely inefficient when: (a) it involves a lot of computations or (b) a huge amount of auxiliary randomness is required.
Revised:  \emph{extremely inefficient when: (a) it involves a lot of computations or (b) a huge amount of auxiliary randomness is required.
Edit intent: coherence
Original:  However, it might be\emph{extremely inefficient when: (a) it involves a lot of computations or (b) a huge amount of auxiliary randomness is required.
Revised:  However, it might be\emph{ when: (a) it involves a lot of computations or (b) a huge amount of auxiliary randomness is required.
Edit intent: clarity
Original:  We study this problem in the computational setting, whereefficiently simulating Z from X becomes possible, if we accept some mistakes and care only about a restricted class of adversaries.
Revised:  We study this problem in the computational setting, where Z from X becomes possible, if we accept some mistakes and care only about a restricted class of adversaries.
Edit intent: clarity
Original:  We prove the following result: for any X\in\{0,1\}^n, any correlated Z\in\{0,1\}^\ell and every choice of (\epsilon, s) there is a randomized h:\{0,1\}^n\rightarrow \{0,1\}^\ell of complexity O(s\cdot 2^{2\ell\epsilon^{-2}) such that Z and h}%DIFDELCMD < {%%% X are (\epsilon,s)-indistinguishable given X.
Revised:  We prove the following result: for any X\in\{0,1\}^n, any correlated Z\in\{0,1\}^\ell and every choice of (\epsilon, s) there is a randomized h:\{0,1\}^n\rightarrow \{0,1\}^\ell of complexity O(s\cdot 2^{2\ell\epsilon^{-2}) such that Z and h}%DIFDELCMD < {%%% are (\epsilon,s)-indistinguishable given X.
Edit intent: fluency
Original: Populations of species in ecosystems are constrained by the availability of resources within their environment.
Revised: Populations of species in ecosystems are often constrained by availability of resources within their environment.
Edit intent: clarity
Original:  In effect this means that a growth of one population, needs to be balanced by the reduction in size of others.
Revised:  In effect this means that a growth of one population, needs to be balanced by comparable reduction in populations of others.
Edit intent: clarity
Original:  The emergent property of the population dynamics in our system are cyclic "diversity waves" triggered by collapses of globally dominating populations.
Revised:  The emergent dynamics of our system is cyclic "diversity waves" triggered by collapses of globally dominating populations.
Edit intent: clarity
Original:  The population diversity in the environment peaks at the beginning of each wave and exponentially decreases afterwards.
Revised:  The population diversity peaks at the beginning of each wave and exponentially decreases afterwards.
Edit intent: clarity
Original:  Population sizes in our system follow a bimodal distribution with the lower peak composed of the recently collapsed or the newly arrived species.
Revised:  Population sizes in our system follow a bimodal distribution with the lower peak formed by populations of recently collapsed or the newly arrived species.
Edit intent: clarity
Original:  In contrast to this, the upper peak of the distribution consists of the surviving species in the current diversity wave.
Revised:  In contrast to this, the upper peak - species that has not yet collapsed in the current diversity wave.
Edit intent: clarity
Original:  The populations of the most abundant species in the upper peak exhibit a scale-free  distribution with a nearly universal exponent of about 1.7.
Revised:  The populations of the most abundant species in the upper peak exhibit a scale-free distribution with a universal exponent of about 1.7.
Edit intent: clarity
Original:  The populations of the most abundant species in the upper peak exhibit a scale-free  distribution with a nearly universal exponent of about 1.7.
Revised:  The populations of the most abundant species in the upper peak exhibit a scale-free distribution with a nearly universal exponent of 1.7.
Edit intent: clarity
Original:  This  paper investigates whether a general phenomenon takes place for multiple communities  without imposing symmetry.
Revised:  This paper investigates whether a general phenomenon takes place for multiple communities , without imposing symmetry.
Edit intent: fluency
Original:  In the general stochastic block model SBM(n,p,Q), n vertices are split into k communities of relative size p_i , and vertices in community i and j connect independently with probability Q_{i,j\}_{i,j \in [k]}} . This paper investigates the partial and exact recovery of communities in the general SBM (in the constant and logarithmic degree regimes), and uses the generality of the results to tackle overlapping communities.
Revised:  In the general stochastic block model SBM(n,p,Q), n vertices are split into k communities of relative size \{p_i\}_{i \in [k] , and vertices in community i and j connect independently with probability Q_{i,j\}_{i,j \in [k]}} . This paper investigates the partial and exact recovery of communities in the general SBM (in the constant and logarithmic degree regimes), and uses the generality of the results to tackle overlapping communities.
Edit intent: clarity
Original:  In the general stochastic block model SBM(n,p,Q), n vertices are split into k communities of relative size p_i , and vertices in community i and j connect independently with probability Q_{i,j\}_{i,j \in [k]}} . This paper investigates the partial and exact recovery of communities in the general SBM (in the constant and logarithmic degree regimes), and uses the generality of the results to tackle overlapping communities.
Revised:  In the general stochastic block model SBM(n,p,Q), n vertices are split into k communities of relative size p_i , and vertices in community i and j connect independently with probability \{Q_{i,j\}_{i,j \in [k]}} . This paper investigates the partial and exact recovery of communities in the general SBM (in the constant and logarithmic degree regimes), and uses the generality of the results to tackle overlapping communities.
Edit intent: fluency
Original:  It is shown that exact recovery in \text{SBM(n,p,\ln(n) Q/n) is solvable if and only if i < j }%DIFDELCMD < \dd%%% (\theta_i,\theta_j) \geq 1, where \theta_i is the i-th column of%DIFDELCMD < \diag%%% (p)Q and%DIFDELCMD < \dd %%% is a generalization of the Chernoff and Hellinger divergence defined by%DIFDELCMD < \dd%%% (x, y):=\max_{t \in [0,1] \sum_{i \in [k]} (tx_i + (1-t)y_i - x_i^t y_i^{1-t}).
Revised:  (n,p,\ln(n) Q/n) is solvable if and only if i < j }%DIFDELCMD < \dd%%% (\theta_i,\theta_j) \geq 1, where \theta_i is the i-th column of%DIFDELCMD < \diag%%% (p)Q and%DIFDELCMD < \dd %%% is a generalization of the Chernoff and Hellinger divergence defined by%DIFDELCMD < \dd%%% (x, y):=\max_{t \in [0,1] \sum_{i \in [k]} (tx_i + (1-t)y_i - x_i^t y_i^{1-t}).
Edit intent: coherence
Original:  It is shown that exact recovery in \text{SBM(n,p,\ln(n) Q/n) is solvable if and only if i < j }%DIFDELCMD < \dd%%% (\theta_i,\theta_j) \geq 1, where \theta_i is the i-th column of%DIFDELCMD < \diag%%% (p)Q and%DIFDELCMD < \dd %%% is a generalization of the Chernoff and Hellinger divergence defined by%DIFDELCMD < \dd%%% (x, y):=\max_{t \in [0,1] \sum_{i \in [k]} (tx_i + (1-t)y_i - x_i^t y_i^{1-t}).
Revised:  It is shown that exact recovery in \text{SBM(n,p,\ln(n) Q/n) is solvable if and only if i < j }%DIFDELCMD < \dd%%% (\theta_i,\theta_j) \geq 1, where \theta_i is the i-th column of%DIFDELCMD < \diag%%% %DIFDELCMD < \dd %%% is a generalization of the Chernoff and Hellinger divergence defined by%DIFDELCMD < \dd%%% (x, y):=\max_{t \in [0,1] \sum_{i \in [k]} (tx_i + (1-t)y_i - x_i^t y_i^{1-t}).
Edit intent: clarity
Original:  To obtain this algorithm, a first-stage algorithm is developed that recovers communities in the constant degree regime with an accuracy guarantee that can be made arbitrarily close to 1 when a prescribed signal-to-noise ratio (defined in term of the spectrum of \diag(p)Q) tends to infinity.
Revised:  To obtain this algorithm, a first-stage algorithm is developed that recovers communities in the constant degree regime with an explicit accuracy bound that can be made arbitrarily close to 1 when a prescribed signal-to-noise ratio (defined in term of the spectrum of \diag(p)Q) tends to infinity.
Edit intent: clarity
Original: A new approach for coordinating components interfaces based on CSP  is presented.
Revised: A new approach for coordinating component interfaces based on CSP is presented.
Edit intent: fluency
Original:  The KPN communication graph thus becomes a graph of interlocked constraints to be satisfied by finding specific instances of the variables.
Revised:  The KPN communication graph thus becomes a graph of interlocked constraints to be satisfied by specific instances of the variables.
Edit intent: clarity
Original:  An algorithm is proposed that solves the satisfaction problem by iterative approximation while generating an adjunct Boolean SAT problem on the way ;
Revised:  We present an algorithm that solves the satisfaction problem by iterative approximation while generating an adjunct Boolean SAT problem on the way ;
Edit intent: clarity
Original: A new approach for coordinating component interfaces based on CSP and SAT is presented .
Revised: We present a new CSP- and SAT-based approach for coordinating component interfaces based on CSP and SAT is presented .
Edit intent: clarity
Original: A new approach for coordinating component interfaces based on CSP and SAT is presented .
Revised: A new approach for coordinating interfaces of distributed stream-connected components provided as closed-source services .
Edit intent: clarity
Original: Despite the growing interest around the emergence of novel technologies, especially from the policy-making perspective , there is still no consensus on what classifies a technology as 'emergent'  .
Revised: There is considerable and growing interest in the emergence of novel technologies, especially from the policy-making perspective , there is still no consensus on what classifies a technology as 'emergent' .
Edit intent: clarity
Original:  We prove the following unconditional result about linear programming (LP) relaxations of the problem: every LP relaxation that approximates vertex cover within a factor of 2-\epsilon has super-polynomially many inequalities.
Revised:  We prove the following unconditional result about linear programming (LP) relaxations of the problem: every LP relaxation that approximates vertex cover within a factor 2-\epsilon has super-polynomially many inequalities.
Edit intent: clarity
Original:  As a direct consequence of our methods, we also establish that LP relaxations  that approximate the independent set problem within any constant factor have super-polynomially many inequalities .
Revised:  As a direct consequence of our methods, we also establish that LP relaxations that approximate the independent set problem within any constant factor have super-polynomial size .
Edit intent: clarity
Original: We show that for any two values \alpha, \beta \in ( 0 ,1) for which \alpha+\beta>1 then there exists a value N so that for all n \geq N , and any binary phylogenetic tree T on n leaves there exists a set of at most n^\alpha \lfloor \rfloor characters that capture T, and for which each character has at most n^\beta\lfloor \rfloor  states.
Revised: We show that for any two values \alpha, \beta \in ( 0 for which \alpha+\beta>1 then there exists a value N so that for all n \geq N , and any binary phylogenetic tree T on n leaves there exists a set of at most n^\alpha \lfloor \rfloor characters that capture T, and for which each character has at most n^\beta\lfloor \rfloor states.
Edit intent: coherence
Original: We show that for any two values \alpha, \beta \in ( 0 ,1) for which \alpha+\beta>1 then there exists a value N so that for all n \geq N , and any binary phylogenetic tree T on n leaves there exists a set of at most n^\alpha \lfloor \rfloor characters that capture T, and for which each character has at most n^\beta\lfloor \rfloor  states.
Revised: We show that for any two values \alpha, \beta \in ( 0 ,1) for which \alpha+\beta>1 then there is a value N so that for all n \geq N , and any binary phylogenetic tree T on n leaves there exists a set of at most n^\alpha \lfloor \rfloor characters that capture T, and for which each character has at most n^\beta\lfloor \rfloor states.
Edit intent: fluency
Original: We show that for any two values \alpha, \beta \in ( 0 ,1) for which \alpha+\beta>1 then there exists a value N so that for all n \geq N , and any binary phylogenetic tree T on n leaves there exists a set of at most n^\alpha \lfloor \rfloor characters that capture T, and for which each character has at most n^\beta\lfloor \rfloor  states.
Revised: We show that for any two values \alpha, \beta \in ( 0 ,1) for which \alpha+\beta>1 then there exists a value N so that for all n \geq N , and any binary phylogenetic tree T on n leaves there is a set of at most n^\alpha \lfloor \rfloor characters that capture T, and for which each character has at most n^\beta\lfloor \rfloor states.
Edit intent: fluency
Original: We show that for any two values \alpha, \beta \in ( 0 ,1) for which \alpha+\beta>1 then there exists a value N so that for all n \geq N , and any binary phylogenetic tree T on n leaves there exists a set of at most n^\alpha \lfloor \rfloor characters that capture T, and for which each character has at most n^\beta\lfloor \rfloor  states.
Revised: We show that for any two values \alpha, \beta \in ( 0 ,1) for which \alpha+\beta>1 then there exists a value N so that for all n \geq N , and any binary phylogenetic tree T on n leaves there exists a set of \lfloor \rfloor characters that capture T, and for which each character has at most n^\beta\lfloor \rfloor states.
Edit intent: fluency
Original: We show that for any two values \alpha, \beta \in ( 0 ,1) for which \alpha+\beta>1 then there exists a value N so that for all n \geq N , and any binary phylogenetic tree T on n leaves there exists a set of at most n^\alpha \lfloor \rfloor characters that capture T, and for which each character has at most n^\beta\lfloor \rfloor  states.
Revised: We show that for any two values \alpha, \beta \in ( 0 ,1) for which \alpha+\beta>1 then there exists a value N so that for all n \geq N , and any binary phylogenetic tree T on n leaves there exists a set of at most n^\alpha \lfloor n^\alpha\rfloor characters that capture T, and for which each character has at most n^\beta\lfloor \rfloor states.
Edit intent: fluency