wanyu/IteraTeR_v2 huggingface dataset:
Original:  We also give models of the axioms that are based on Gaussian functions, that allow for exact computations and automated tests of signal algorithm properties.
Revised:  We give models of the axioms that are based on Gaussian functions, that allow for exact computations and automated tests of signal algorithm properties.
Edit intent: clarity
Original: The process of comparison of computer generated protein structural models is an important element of protein structure prediction.
Revised: The comparison of computer generated protein structural models is an important element of protein structure prediction.
Edit intent: clarity
Original:  It has many uses including model quality evaluation, selection of the final models from a large set of candidates or optimisation of parameters of energy functions used in template free modelling and refinement.
Revised:  It has many uses including model quality evaluation, selection of the final models from a large set of candidates or optimisation of parameters of energy functions used in template-free modelling and refinement.
Edit intent: fluency
Original:  Although many protein comparison methods are available online on numerous web servers, their ability to handle a large scale model comparison is often very limited.
Revised:  Although many protein comparison methods are available online on numerous web servers, they are not well suited for large scale model comparison is often very limited.
Edit intent: clarity
Original:  In this paper we present a package for Mathematica computing system harnessing a specific piece of hardware, namely a Quantis quantum random number generator (QRNG), for investigating statistical properties of quantum states.
Revised:  In this paper we present a package for Mathematica computing system harnessing a specific piece of hardware, namely Quantis quantum random number generator (QRNG), for investigating statistical properties of quantum states.
Edit intent: fluency
Original:  The described package implements a number of functions for generating random states, which uses a Quantis QRNG as a source of randomness.
Revised:  The described package implements a number of functions for generating random states, which use Quantis QRNG as a source of randomness.
Edit intent: fluency
Original:  For decades, CSE has been misunderstood to require massive computers, whereas breakthroughs in CSE have historically been the mathematical programs of computing rather than the machines themselves .
Revised:  For decades, CSE has been misunderstood to require massive computers, whereas breakthroughs in CSE have historically been the mathematical programs of computing rather than the machines that run the programs .
Edit intent: clarity
Original: Computational science and engineering (CSE) has been misunderstood to require massive computers, whereas breakthroughs in CSE have historically been the mathematical programs of computing rather than the machines that run the programs.
Revised: Computational science and engineering (CSE) has been misunderstood to advance with the construction of enormous computers. To the contrary, the historical record demonstrates that innovations in CSE come from improvements to the mathematics embodied by computer programs.
Edit intent: clarity
Original:  Numerical results show that the proposed algorithm achieves up to 18\%  performance improvement than the static channel recommendation scheme and 10\% performance improvement than the Q-learning method, and is robust to channel dynamics.
Revised:  Numerical results show that the proposed algorithms achieve up to 18\% performance improvement than the static channel recommendation scheme and 10\% performance improvement than the Q-learning method, and is robust to channel dynamics.
Edit intent: fluency
Original: Social, biological and economic networks evolve with recurrent fragmentation and re-formation, often explained in terms of external perturbations.
Revised: Social, biological and economic networks grow and decline with occasional fragmentation and re-formation, often explained in terms of external perturbations.
Edit intent: clarity
Original:  We show that these phenomena can be a direct consequence of imitation and endogenous conflicts between 'cooperators' and 'defectors'.
Revised:  We show that these phenomena can be a direct consequence of simple imitation and internal conflicts between 'cooperators' and 'defectors'.
Edit intent: clarity
Original:  We employ a game-theoretic model of dynamic network formation , where prosperous individuals are more likely to be selected as role-models by newcomers who imitate their strategies and their connections .
Revised:  We employ a game-theoretic model of dynamic network formation where successful individuals are more likely to be selected as role-models by newcomers who imitate their strategies and their connections .
Edit intent: clarity
Original:  We employ a game-theoretic model of dynamic network formation , where prosperous individuals are more likely to be selected as role-models by newcomers who imitate their strategies and their connections .
Revised:  We employ a game-theoretic model of dynamic network formation , where prosperous individuals are more likely to be imitated by newcomers who imitate their strategies and their connections .
Edit intent: clarity
Original:  We employ a game-theoretic model of dynamic network formation , where prosperous individuals are more likely to be selected as role-models by newcomers who imitate their strategies and their connections .
Revised:  We employ a game-theoretic model of dynamic network formation , where prosperous individuals are more likely to be selected as role-models by newcomers who adopt their strategies and their connections .
Edit intent: clarity
Original:  We employ a game-theoretic model of dynamic network formation , where prosperous individuals are more likely to be selected as role-models by newcomers who imitate their strategies and their connections .
Revised:  We employ a game-theoretic model of dynamic network formation , where prosperous individuals are more likely to be selected as role-models by newcomers who imitate their strategies and copy their social network .
Edit intent: clarity
Original:  Once the network is fragmented , it can be reconstructed by a new invasion of cooperators .
Revised:  Once the network is fragmented it can be reconstructed by a new invasion of cooperators .
Edit intent: fluency
Original:  Second, we develop an extension of the approach to a call-by-value \lambda-calculus with multithreading and side effects.
Revised:  Second, we develop an extension of the approach to a call-by-value lambda-calculus with multithreading and side effects.
Edit intent: fluency
Original:  These automata models yield decidability of the membership problem.
Edit intent: coherence
Original:  In this paper, we analyze the stochastic Kronecker graph model (SKG), which is the foundation of the Graph500 supercomputer benchmark due to its many favorable properties and easy parallelization.
Revised:  In this paper, we analyze the stochastic Kronecker graph model (SKG), which is the foundation of the Graph500 supercomputer benchmark due to its favorable properties and easy parallelization.
Edit intent: clarity
Original: We show that for all \delta>0 and arbitrarily small \epsilon>0, there exists a graph property \Pi (which depends on \epsilon) such that \epsilon-testing \Pi requires qadaptive queries, while any non-adaptive algorithm requires at least q\Theta  ^{ 2-\delta } queries .
Revised: We show that for all \delta>0 and arbitrarily small \epsilon>0, there exists a graph property \Pi (which depends on \epsilon) such that \epsilon-testing \Pi has non-adaptive algorithm requires at least q\Theta ^{ 2-\delta } queries .
Edit intent: clarity
Original: We show that for all \delta>0 and arbitrarily small \epsilon>0, there exists a graph property \Pi (which depends on \epsilon) such that \epsilon-testing \Pi requires qadaptive queries, while any non-adaptive algorithm requires at least q\Theta  ^{ 2-\delta } queries .
Revised: We show that for all \delta>0 and arbitrarily small \epsilon>0, there exists a graph property \Pi (which depends on \epsilon) such that \epsilon-testing \Pi requires qadaptive queries, while any non-adaptive query complexity Q=\Theta ^{ 2-\delta } queries .
Edit intent: clarity
Original:  In this paper, we prove that the corresponding adaptive query complexity is \~O(\epsilon^{-1 , we show that for all H, testing whether G is a collection of blow-ups of H and has maximum degree c\epsilon N can be done adaptively using only O(\epsilon^{-1}\lg ^3{\frac{1{\epsilon}}) queries} }) adaptive queries or O(\epsilon^{-2+1/(\delta+2)}+\epsilon^{-2+2/W}) non-adaptive queries, where \delta=\Delta(H) is the maximum degree of H and W<}\abs{H} .
Revised:  In this paper, we prove that the corresponding adaptive query complexity is \~O(\epsilon^{-1 , we show that for all H, testing whether G is a collection of blow-ups of H and has maximum degree c\epsilon N requires only O(\epsilon^{-1}\lg ^3{\frac{1{\epsilon}}) queries} }) adaptive queries or O(\epsilon^{-2+1/(\delta+2)}+\epsilon^{-2+2/W}) non-adaptive queries, where \delta=\Delta(H) is the maximum degree of H and W<}\abs{H} .
Edit intent: clarity
Original:  In this paper, we prove that the corresponding adaptive query complexity is \~O(\epsilon^{-1 , we show that for all H, testing whether G is a collection of blow-ups of H and has maximum degree c\epsilon N can be done adaptively using only O(\epsilon^{-1}\lg ^3{\frac{1{\epsilon}}) queries} }) adaptive queries or O(\epsilon^{-2+1/(\delta+2)}+\epsilon^{-2+2/W}) non-adaptive queries, where \delta=\Delta(H) is the maximum degree of H and W<}\abs{H} .
Revised:  In this paper, we prove that the corresponding adaptive query complexity is \~O(\epsilon^{-1 , we show that for all H, testing whether G is a collection of blow-ups of H and has maximum degree c\epsilon N can be done adaptively using only O(\epsilon^{-1}\lg ^3{\frac{1{\epsilon}}) queries} ^3{\epsilon^{-1}) adaptive queries or O(\epsilon^{-2+1/(\delta+2)}+\epsilon^{-2+2/W}) non-adaptive queries, where \delta=\Delta(H) is the maximum degree of H and W<}\abs{H} .
Edit intent: fluency
Original:  This also gives evidence that the canonical transformation of Goldreich and Trevisan (\mbox{ canonical-testers}0pt ) is essentially optimal when converting an adaptive property tester to a } non-adaptive query complexity is \Omega(\epsilon^{-2+2/t), even under the promise that G has maximum degree c\epsilon N for a fixed constant c.
Revised:  This also gives evidence that the canonical transformation of Goldreich and Trevisan (\mbox{ canonical-testers}0pt ) is essentially optimal when converting an adaptive property tester to a } non-adaptive ), even under the promise that G has maximum degree c\epsilon N for a fixed constant c.
Edit intent: clarity
Original:  Specifically, we show that for all H, testing whether G is a collection of blow-ups of H and has maximum degree c\epsilon N requires only O(\epsilon ^{-1\lg^3{\epsilon^{-1}}) adaptive queries or O(\epsilon^{-2+1/(\delta+2)}+\epsilon^{-2+2/W}) non-adaptive queries, where \delta=\Delta(H) is the maximum degree of H and W<}%DIFDELCMD < H%%% ^2 is a bound on the size of witnesses against  H.
Revised:  Specifically, we show that for all H, testing whether G is a collection of blow-ups of H and has maximum degree c\epsilon N requires only O(\epsilon \lg^3{\epsilon^{-1}}) adaptive queries or O(\epsilon^{-2+1/(\delta+2)}+\epsilon^{-2+2/W}) non-adaptive queries, where \delta=\Delta(H) is the maximum degree of H and W<}%DIFDELCMD < H%%% ^2 is a bound on the size of witnesses against H.
Edit intent: coherence
Original:  Specifically, we show that for all H, testing whether G is a collection of blow-ups of H and has maximum degree c\epsilon N requires only O(\epsilon ^{-1\lg^3{\epsilon^{-1}}) adaptive queries or O(\epsilon^{-2+1/(\delta+2)}+\epsilon^{-2+2/W}) non-adaptive queries, where \delta=\Delta(H) is the maximum degree of H and W<}%DIFDELCMD < H%%% ^2 is a bound on the size of witnesses against  H.
Revised:  Specifically, we show that for all H, testing whether G is a collection of blow-ups of H and has maximum degree c\epsilon N requires only O(\epsilon ^{-1\lg^3{\epsilon^{-1}}) adaptive queries or O(\epsilon^{-2+1/(\delta+2)}+\epsilon^{-2+2/W}) non-adaptive queries, where \delta=\Delta(H) is the maximum degree of H and W<}%DIFDELCMD < H%%% N) and being a H.
Edit intent: clarity
Original:  Specifically, we show that for all H, testing whether G is a collection of blow-ups of H and has maximum degree c\epsilon N requires only O(\epsilon ^{-1\lg^3{\epsilon^{-1}}) adaptive queries or O(\epsilon^{-2+1/(\delta+2)}+\epsilon^{-2+2/W}) non-adaptive queries, where \delta=\Delta(H) is the maximum degree of H and W<}%DIFDELCMD < H%%% ^2 is a bound on the size of witnesses against  H.
Revised:  Specifically, we show that for all H, testing whether G is a collection of blow-ups of H and has maximum degree c\epsilon N requires only O(\epsilon ^{-1\lg^3{\epsilon^{-1}}) adaptive queries or O(\epsilon^{-2+1/(\delta+2)}+\epsilon^{-2+2/W}) non-adaptive queries, where \delta=\Delta(H) is the maximum degree of H and W<}%DIFDELCMD < H%%% ^2 is a bound on the size of witnesses againstblow-up collection H.
Edit intent: clarity
Original: We investigate the impact of cooperative relaying on uplink and downlink multi-user (MU) wireless video transmission .
Revised: We investigate the impact of cooperative relaying on uplink and downlink multi-user (MU) wireless video transmissions .
Edit intent: fluency
Original:  Our simulation results demonstrate that integrating cooperative decisions into the MUMDP optimization increases the resource price in congested networks and decreases the price in uncongested ones .
Revised:  Our simulation results demonstrate that integrating cooperative decisions into the MU-MDP optimization can increase the resource price in congested networks and decreases the price in uncongested ones .
Edit intent: clarity
Original:  Additionally, our results show that cooperation allows users with feeble direct signals to achieve improvements in video quality on the order of 5 - 10 dB peak signal-to-noise ratio  , with less than 0.8 dB quality loss by users with strong direct signals  .
Revised:  Additionally, our results show that cooperation allows users with feeble direct signals to achieve improvements in video quality on the order of 5-10 dB peak signal-to-noise ratio , with less than 0.8 dB quality loss by users with strong direct signals .
Edit intent: fluency
Original:  Market impact is empirically observed to be a concave function of metaorder size, i.e.  the impact per share of large metaorders is smaller than that of small metaorders.
Revised:  Market impact is empirically observed to be a concave function of metaorder size, i.e. , the impact per share of large metaorders is smaller than that of small metaorders.
Edit intent: fluency
Original:  Based on our core formalization, we develop a library of polytime functions that can be reused to build more complex ones.
Revised:  Based on our core formalization, we have started developing a library of polytime functions that can be reused to build more complex ones.
Edit intent: clarity
Original:  In particular, we ask how a given property on the evolution of the network can be formally proven as necessary or sufficient for a given algorithm.
Revised:  In particular, we ask how a given property on the evolution of the network can be rigorously proven as necessary or sufficient for a given algorithm.
Edit intent: clarity
Original:  Such a combination makes it possible to express fine-grained properties on the network dynamics, then examine what impact those properties have on the possible outcomes of an execution .
Revised:  Such a combination makes it possible to express fine-grained properties on the network dynamics, then examine what impact those properties have on the execution at a precise, intertwined, level .
Edit intent: clarity
Original:  We illustrate the use of this framework through the analysis of three simple algorithms, then discuss general implications of this work, which include (i) the possibility to compare distributed algorithms on the basis of their topological requirements, (ii) a formal classification of dynamic networks based on these requirements, and (iii) the potential for mechanization induced by our framework, which we believe opens a path towards automated analysis and decision support in dynamic networks.
Revised:  We illustrate the use of this framework through the analysis of three simple algorithms, then discuss general implications of this work, which include (i) the possibility to compare distributed algorithms on the basis of their topological requirements, (ii) a formal hierarchy of dynamic networks based on these requirements, and (iii) the potential for mechanization induced by our framework, which we believe opens a path towards automated analysis and decision support in dynamic networks.
Edit intent: clarity
Original:  We illustrate the use of this framework through the analysis of three simple algorithms, then discuss general implications of this work, which include (i) the possibility to compare distributed algorithms on the basis of their topological requirements, (ii) a formal classification of dynamic networks based on these requirements, and (iii) the potential for mechanization induced by our framework, which we believe opens a path towards automated analysis and decision support in dynamic networks.
Revised:  We illustrate the use of this framework through the analysis of three simple algorithms, then discuss general implications of this work, which include (i) the possibility to compare distributed algorithms on the basis of their topological requirements, (ii) a formal classification of dynamic networks based on these requirements, and (iii) the potential for mechanization induced by our framework, which we believe opens a door towards automated analysis and decision support in dynamic networks.
Edit intent: clarity
Original:  To answer a query " x\in A?" we allow to read the whole cached word and only one bit from the main storage.
Revised:  To answer a query " Is x in A?" we allow to read the whole cached word and only one bit from the main storage.
Edit intent: clarity
Original: In this paper, the author defines Generalized Unique Game Problem (GUGP), where weights of the edges are allowed to be negative.
Revised: In this paper, the authors define Generalized Unique Game Problem (GUGP), where weights of the edges are allowed to be negative.
Edit intent: fluency
Original:  The author investigates the counterparts of the Unique Game Conjecture for the two types of generalized unique game problems.
Revised:  The authors investigate the counterparts of the Unique Game Conjecture for the two types of generalized unique game problems.
Edit intent: fluency
Original:  The author proves Unique Game Conjecture holds false on GUGP-NWA by giving a factor 2 approximation algorithm for Max GUGP-NWA, and Unique Game Conjecture holds true on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1) . The author poses an open problem whether Unique Game Conjecture holds true on GUGP-PWT(\rho) with 0<\rho<1.
Revised:  The authors prove Unique Game Conjecture holds false on GUGP-NWA by giving a factor 2 approximation algorithm for Max GUGP-NWA, and Unique Game Conjecture holds true on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1) . The author poses an open problem whether Unique Game Conjecture holds true on GUGP-PWT(\rho) with 0<\rho<1.
Edit intent: clarity
Original:  The author proves Unique Game Conjecture holds false on GUGP-NWA by giving a factor 2 approximation algorithm for Max GUGP-NWA, and Unique Game Conjecture holds true on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1) . The author poses an open problem whether Unique Game Conjecture holds true on GUGP-PWT(\rho) with 0<\rho<1.
Revised:  The author proves Unique Game Conjecture holds false on GUGP-NWA by giving a factor 2 approximation algorithm for Max GUGP-NWA, Unique Game Conjecture holds true on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1) . The author poses an open problem whether Unique Game Conjecture holds true on GUGP-PWT(\rho) with 0<\rho<1.
Edit intent: fluency
Original:  The authors investigate the counterparts of the Unique Game Conjecture for the two types of generalized unique game problems .
Revised:  The authors investigate the counterpart of the Unique Game Conjecture for the two types of generalized unique game problems .
Edit intent: fluency
Original:  The authors prove Unique Game Conjecture holds false on GUGP-NWA by giving a factor 2 approximation algorithm for Max GUGP-NWA, Unique Game Conjecture holds true on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1), and Unique Game Conjecture holds true on GUGP-PWT(1/2) if the 2-to-1 Conjecture holds true.
Revised:  The authors prove Unique Game Conjecture holds true on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1), and Unique Game Conjecture holds true on GUGP-PWT(1/2) if the 2-to-1 Conjecture holds true.
Edit intent: coherence
Original: In this paper, the authors define Generalized Unique Game Problem (GUGP), where weights of the edges are allowed to be negative.
Revised: In this paper, the author defines Generalized Unique Game Problem (GUGP), where weights of the edges are allowed to be negative.
Edit intent: fluency
Original:  Focuses are made on two special types of GUGP  , GUGP-NWA, where the weights of all edges are negative, and GUGP-PWT(\rho), where the total weight of all edges are positive and the negative/positive ratio is at most \rho.
Revised:  Two special types of GUGP , GUGP-NWA, where the weights of all edges are negative, and GUGP-PWT(\rho), where the total weight of all edges are positive and the negative/positive ratio is at most \rho.
Edit intent: clarity
Original:  Focuses are made on two special types of GUGP  , GUGP-NWA, where the weights of all edges are negative, and GUGP-PWT(\rho), where the total weight of all edges are positive and the negative/positive ratio is at most \rho.
Revised:  Focuses are made on two special types of GUGP are illuminated , GUGP-NWA, where the weights of all edges are negative, and GUGP-PWT(\rho), where the total weight of all edges are positive and the negative/positive ratio is at most \rho.
Edit intent: clarity
Original:  Focuses are made on two special types of GUGP  , GUGP-NWA, where the weights of all edges are negative, and GUGP-PWT(\rho), where the total weight of all edges are positive and the negative/positive ratio is at most \rho.
Revised:  Focuses are made on two special types of GUGP , GUGP-NWA, where the weights of all edges are negative, and GUGP-PWT(\rho), where the total weight of all edges are positive and the negative-positive ratio is at most \rho.
Edit intent: clarity
Original:  The authors investigate the counterpart of the Unique Game Conjecture on GUGP-PWT(\rho).
Revised:  The author investigates the counterpart of the Unique Game Conjecture on GUGP-PWT(\rho).
Edit intent: fluency
Original:  The authors prove Unique Game Conjecture holds true on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1) , and Unique Game Conjecture holds true on GUGP-PWT(1/2)  if the 2-to-1 Conjecture holds true.
Revised:  The author shows that Unique Game Conjecture holds true on GUGP-PWT(1) by reducing the parallel repetition of Max 3-Cut Problem to GUGP-PWT(1) , and Unique Game Conjecture holds true on GUGP-PWT(1/2) if the 2-to-1 Conjecture holds true.
Edit intent: clarity