wanyu/IteraTeR_v2 huggingface dataset:
Original:  Further, and in a stark departure from other implementations of multi-level Monte Carlo, we show how to make use of the existence of exact algorithms to produce an unbiased estimator that is significantly less computationally expensive than the usual unbiased estimator arising from exact algorithms in conjunction with crude Monte Carlo.
Revised:  Further, and in a stark departure from other implementations of multi-level Monte Carlo, we show how to produce an unbiased estimator that is significantly less computationally expensive than the usual unbiased estimator arising from exact algorithms in conjunction with crude Monte Carlo.
Edit intent: clarity
Original:  We thereby show that the basic computational complexity of the Gillespie/ stochastic simulation algorithm / tau-leaping approaches can be dramatically improved in a manner that can be quantified precisely .
Revised:  We thereby dramatically improve, in a quantifiable manner, the basic computational complexity of the Gillespie/ stochastic simulation algorithm / tau-leaping approaches can be dramatically improved in a manner that can be quantified precisely .
Edit intent: clarity
Original:  The prevalent pentamer structure, the asymmetry of Lov\'en 's rule and the variable location of the periproct and madrepore present enormous difficulties in homologizing structures across the major clades, despite the excellent fossil record.
Revised:  The prevalent pentamer structure, the asymmetry of Loven 's rule and the variable location of the periproct and madrepore present enormous difficulties in homologizing structures across the major clades, despite the excellent fossil record.
Edit intent: fluency
Original:  The theory provides fundamental insight into the M-plane and the Ubisch', Lov\'en 's and Carpenter's planes and generalizes them for all echinoderms.
Revised:  The theory provides fundamental insight into the M-plane and the Ubisch', Loven 's and Carpenter's planes and generalizes them for all echinoderms.
Edit intent: fluency
Original:  We present three algorithms for computing crosscap number that offer varying trade-offs between precision and speed: (i) an algorithm based on Hilbert basis enumeration and (ii) an algorithm based on exact integer programming, both of which either compute the solution precisely or reduce it to two possible values, and (iii) a fast but limited precision integer programming algorithm that bounds the solution from above.
Revised:  We present three methods for computing crosscap number that offer varying trade-offs between precision and speed: (i) an algorithm based on Hilbert basis enumeration and (ii) an algorithm based on exact integer programming, both of which either compute the solution precisely or reduce it to two possible values, and (iii) a fast but limited precision integer programming algorithm that bounds the solution from above.
Edit intent: clarity
Original:  By running the final algorithm we are able to make significant improvements to the current status of crosscap numbers in tables of knots with \leq 12 crossings .
Revised:  The first two algorithms advance the theoretical state of the art, but remain intractable for practical use. The third algorithm is fast and effective, which we show in a practical setting by making significant improvements to the current status of crosscap numbers in tables of knots with \leq 12 crossings .
Edit intent: coherence
Original:  By running the final algorithm we are able to make significant improvements to the current status of crosscap numbers in tables of knots with \leq 12 crossings .
Revised:  By running the final algorithm we are able to make significant improvements to the current knowledge of crosscap numbers in tables of knots with \leq 12 crossings .
Edit intent: clarity
Original:  By running the final algorithm we are able to make significant improvements to the current status of crosscap numbers in tables of knots with \leq 12 crossings .
Revised:  By running the final algorithm we are able to make significant improvements to the current status of crosscap numbers in knot tables .
Edit intent: clarity
Original:  Each agent requests some number of resources x_i and specifies its true valuation v _i(x_i) for receiving them, to a central entity.
Revised:  Each agent requests a number of resources x_i and specifies its true valuation v _i(x_i) for receiving them, to a central entity.
Edit intent: clarity
Original:  Each agent requests some number of resources x_i and specifies its true valuation v _i(x_i) for receiving them, to a central entity.
Revised:  Each agent requests some number of resources x_i and reports a valuation _i(x_i) for receiving them, to a central entity.
Edit intent: clarity
Original: {\em   The pairs (x_i, v _i(x_i)) can be thought of as size-value pairs defining a knapsack problem with capacity m.
Revised: {\em lower The pairs (x_i, v _i(x_i)) can be thought of as size-value pairs defining a knapsack problem with capacity m.
Edit intent: fluency
Original: {\em   The pairs (x_i, v _i(x_i)) can be thought of as size-value pairs defining a knapsack problem with capacity m.
Revised: {\em The pairs (x_i, _i(x_i)) can be thought of as size-value pairs defining a knapsack problem with capacity m.
Edit intent: clarity
Original:  The central entity must use some publicly-known mechanism to solve this knapsack problem, deciding which requests to satisfy in order to maximize the social welfare.
Revised:  A publicly-known mechanism to solve this knapsack problem, deciding which requests to satisfy in order to maximize the social welfare.
Edit intent: clarity
Original:  The central entity must use some publicly-known mechanism to solve this knapsack problem, deciding which requests to satisfy in order to maximize the social welfare.
Revised:  The central entity must use some publicly-known algorithm is used to solve this knapsack problem, deciding which requests to satisfy in order to maximize the social welfare.
Edit intent: clarity
Original:  Instead, and somewhat surprisingly, we show that a simpler mechanism , based on the knapsack {\it highest ratio greedy} algorithm , provides a PoA of 2.
Revised:  Instead, and somewhat surprisingly, we show that a simple mechanism based on the knapsack {\it highest ratio greedy} algorithm , provides a PoA of 2.
Edit intent: fluency
Original:  We also give an algorithm computing a Nash equilibrium strategy profile in O( (n\log m)^2) time.
Revised:  We also give an algorithm that computes a Nash equilibrium strategy profile in O( (n\log m)^2) time.
Edit intent: fluency
Original:  We also give an algorithm computing a Nash equilibrium strategy profile in O( (n\log m)^2) time.
Revised:  We also give an algorithm computing a Nash equilibrium strategy profile in O( n^2 \log^2 m) time.
Edit intent: clarity
Original:  Our primary algorithmic result shows that extending the mechanism to multiple rounds can arbitrarily strengthen the guarantee.
Revised:  Our primary algorithmic result shows that an extension of the mechanism to multiple rounds can arbitrarily strengthen the guarantee.
Edit intent: fluency
Original:  We present computational results on our cortical model, on a model that is random in the Erd\H{os-R\'{e}nyi }  sense, and on a structurally deterministic model.
Revised:  We present computational results on our cortical model, on a model that is random in the s-R\'{e}nyi } sense, and on a structurally deterministic model.
Edit intent: clarity
Original:  Here we present a theoretical study of these issues on a cortical model we introduced earlier [ A. Nathan and V. C. Barbosa, Phys . Rev . E 81 , 021916 (2010) ].
Revised:  Here we present a theoretical study of these issues on a cortical model we introduced earlier [ A. Nathan and V. C. Barbosa, Phys . Rev . E 81 : 021916 (2010) ].
Edit intent: fluency
Original:  Here we present a theoretical study of these issues on a cortical model we introduced earlier [ A. Nathan and V. C. Barbosa, Phys . Rev . E 81 , 021916 (2010) ].
Revised:  Here we present a theoretical study of these issues on a cortical model we introduced earlier [ A. Nathan and V. C. Barbosa, Phys . Rev . E 81 , 021916 ].
Edit intent: coherence
Original:  We start with the definition of two synchronization measures that aim to capture the synchronization possibilities offered by the model regarding both the accumulation of potential at the neurons ' membranes and the spiking activity of the neurons.
Revised:  We start with the definition of two synchronization measures that aim to capture the synchronization possibilities offered by the model regarding both the overall spiking activity of the neurons and the spiking activity of the neurons.
Edit intent: clarity
Original:  We present computational results on our cortical model, on a model that is random in the Erdos-Renyis-R\'enyi } sense, and on a structurally deterministic model.
Revised:  We present computational results on our cortical model, on a model that is random in the Erd\H{os-R\'enyi } sense, and on a structurally deterministic model.
Edit intent: clarity
Original:  We introduce a new technique for proving such bounds, called symmetrization, which is natural, intuitive, and relatively easy to use in comparison to other techniques for proving such bounds such as theicost method \mbox{ BYJKS02 . For example, for the problem where each of k players gets a bit-vector of length n, and the goal is to compute the coordinate-wise XOR of these vectors, we prove a tight lower bounds of \Omega(nk) in the blackboard model.
Revised:  We introduce a new technique for proving such bounds, called symmetrization, which is natural, intuitive, and often easy to use in comparison to other techniques for proving such bounds such as theicost method \mbox{ BYJKS02 . For example, for the problem where each of k players gets a bit-vector of length n, and the goal is to compute the coordinate-wise XOR of these vectors, we prove a tight lower bounds of \Omega(nk) in the blackboard model.
Edit intent: clarity
Original:  We introduce a new technique for proving such bounds, called symmetrization, which is natural, intuitive, and relatively easy to use in comparison to other techniques for proving such bounds such as theicost method \mbox{ BYJKS02 . For example, for the problem where each of k players gets a bit-vector of length n, and the goal is to compute the coordinate-wise XOR of these vectors, we prove a tight lower bounds of \Omega(nk) in the blackboard model.
Revised:  We introduce a new technique for proving such bounds, called symmetrization, which is natural, intuitive, and relatively easy to use icost method \mbox{ BYJKS02 . For example, for the problem where each of k players gets a bit-vector of length n, and the goal is to compute the coordinate-wise XOR of these vectors, we prove a tight lower bounds of \Omega(nk) in the blackboard model.
Edit intent: coherence
Original:  We introduce a new technique for proving such bounds, called symmetrization, which is natural, intuitive, and relatively easy to use in comparison to other techniques for proving such bounds such as theicost method \mbox{ BYJKS02 . For example, for the problem where each of k players gets a bit-vector of length n, and the goal is to compute the coordinate-wise XOR of these vectors, we prove a tight lower bounds of \Omega(nk) in the blackboard model.
Revised:  We introduce a new technique for proving such bounds, called symmetrization, which is natural, intuitive, and relatively easy to use in comparison to other techniques for proving such bounds such as the \mbox{ BYJKS02 . For example, for the problem where each of k players gets a bit-vector of length n, and the goal is to compute the coordinate-wise XOR of these vectors, we prove a tight lower bounds of \Omega(nk) in the blackboard model.
Edit intent: clarity
Original:  We introduce a new technique for proving such bounds, called symmetrization, which is natural, intuitive, and relatively easy to use in comparison to other techniques for proving such bounds such as theicost method \mbox{ BYJKS02 . For example, for the problem where each of k players gets a bit-vector of length n, and the goal is to compute the coordinate-wise XOR of these vectors, we prove a tight lower bounds of \Omega(nk) in the blackboard model.
Revised:  We introduce a new technique for proving such bounds, called symmetrization, which is natural, intuitive, and relatively easy to use in comparison to other techniques for proving such bounds such as theicost method . For example, for the problem where each of k players gets a bit-vector of length n, and the goal is to compute the coordinate-wise XOR of these vectors, we prove a tight lower bounds of \Omega(nk) in the blackboard model.
Edit intent: coherence
Original:  The obtained communication lower bounds imply new lower bounds in thefunctional monitoring model \mbox{ CMY080pt (also called the }distributed streaming model ) . All of our lower bounds allow randomized communication protocols with two-sided error.
Revised:  The obtained communication lower bounds imply new lower bounds in the \mbox{ CMY080pt (also called the }distributed streaming model ) . All of our lower bounds allow randomized communication protocols with two-sided error.
Edit intent: clarity
Original:  The obtained communication lower bounds imply new lower bounds in thefunctional monitoring model \mbox{ CMY080pt (also called the }distributed streaming model ) . All of our lower bounds allow randomized communication protocols with two-sided error.
Revised:  The obtained communication lower bounds imply new lower bounds in thefunctional monitoring model \mbox{ CMY080pt (also called the } ) . All of our lower bounds allow randomized communication protocols with two-sided error.
Edit intent: clarity
Original:  The obtained communication lower bounds imply new lower bounds in thefunctional monitoring model \mbox{ CMY080pt (also called the }distributed streaming model ) . All of our lower bounds allow randomized communication protocols with two-sided error.
Revised:  The obtained communication lower bounds imply new lower bounds in thefunctional monitoring model \mbox{ CMY080pt (also called the }distributed streaming model . All of our lower bounds allow randomized communication protocols with two-sided error.
Edit intent: fluency
Original:  We apply , as an example, this method to establish that the threshold r_{k}  of monotone 1-in-k-SAT is \log k/k\leq r_{k}\leq\log^{2}k/k 
Revised:  We apply , as an example, this method to establish that the threshold r_{k} of monotone 1-in-k-SAT is \log k/k\leq r_{k}\leq\log^{2}k/k .
Edit intent: fluency
Original: Finding the parameter values of differential equation models from data is an important part of the modelling process . Large models and sparse data often make the parameters very difficult to find .
Revised: Motivation: Estimating parameter values of differential equation models from data is an important part of the modelling process . Large models and sparse data often make the parameters very difficult to find .
Edit intent: clarity
Original: Finding the parameter values of differential equation models from data is an important part of the modelling process . Large models and sparse data often make the parameters very difficult to find .
Revised: Finding the parameter values of models from data is an important part of the modelling process . Large models and sparse data often make the parameters very difficult to find .
Edit intent: clarity
Original: Finding the parameter values of differential equation models from data is an important part of the modelling process . Large models and sparse data often make the parameters very difficult to find .
Revised: Finding the parameter values of differential equation models from data is a critical part of the modelling process . Large models and sparse data often make the parameters very difficult to find .
Edit intent: clarity
Original: Finding the parameter values of differential equation models from data is an important part of the modelling process . Large models and sparse data often make the parameters very difficult to find .
Revised: Finding the parameter values of differential equation models from data is an important part of the modelling process , particularly in biological systems where large numbers of parameters need to be estimated from sparse and noisy data sets .
Edit intent: clarity
Original:  Over the years there have been a number of methods proposed to solve this problem, some with good results but there is still plenty of room for improvement.
Revised:  Over the years there have been a number of methods proposed to solve this complex optimisation problem, with good results but there is still plenty of room for improvement.
Edit intent: clarity
Original:  In this work, we combine ideas from sequential Monte Carlo methods and genetic algorithms to create a new method to fit model parameters.
Revised:  In this work, we develop an algorithm for model parameter fitting that combines ideas from sequential Monte Carlo methods and genetic algorithms to create a new method to fit model parameters.
Edit intent: clarity
Original:  We test our method in different models with real and simulated data and it is able to retrieve good parameter values .
Revised:  The method refines iteratively a sequence of parameter distributions through a combination of local optimisation with partial resampling from a historical prior defined over the support of all the iterations. We exemplify our method with three biological models using both simulated and real experimental data and retrieve efficiently the parameter values even in the absence of good a priori estimates. Availability: Matlab code available from the authors upon request .
Edit intent: clarity
Original: Motivation: Estimating parameter values of models from data is a critical part of the modelling process, particularly in biological systems where large numbers of parameters need to be estimated from sparse and noisy data sets.
Revised: Motivation: Estimating parameters from data is a critical part of the modelling process, particularly in biological systems where large numbers of parameters need to be estimated from sparse and noisy data sets.
Edit intent: clarity
Original: Motivation: Estimating parameter values of models from data is a critical part of the modelling process, particularly in biological systems where large numbers of parameters need to be estimated from sparse and noisy data sets.
Revised: Motivation: Estimating parameter values of models from data is a key stage of the modelling process, particularly in biological systems where large numbers of parameters need to be estimated from sparse and noisy data sets.
Edit intent: clarity
Original: Motivation: Estimating parameter values of models from data is a critical part of the modelling process, particularly in biological systems where large numbers of parameters need to be estimated from sparse and noisy data sets.
Revised: Motivation: Estimating parameter values of models from data is a critical part of the modelling process, particularly in biological systems where many parameters need to be estimated from sparse and noisy data sets.
Edit intent: clarity
Original:  Over the years, a variety of methods based on different heuristics have been proposed to solve this complex optimisation problem, with good results in some cases yet with limitations in the biological setting.
Revised:  Over the years, a variety of heuristics have been proposed to solve this complex optimisation problem, with good results in some cases yet with limitations in the biological setting.
Edit intent: clarity
Original:  Results: In this work, we develop an algorithm for model parameter fitting that combines ideas from  sequential Monte Carlo , evolutionary algorithms and direct search optimisation.
Revised:  Results: In this work, we develop an algorithm for model parameter fitting that combines ideas from sequential Monte Carlo and direct search optimisation.
Edit intent: clarity
Original:  The method refines iteratively a sequence of parameter distributions through a combination of local optimisation with partial resampling from a historical prior defined over the support of all the iterations.
Revised:  The method refines iteratively a sequence of parameter distributions through local optimisation combined with partial resampling from a historical prior defined over the support of all the iterations.
Edit intent: fluency
Original:  The method refines iteratively a sequence of parameter distributions through a combination of local optimisation with partial resampling from a historical prior defined over the support of all the iterations.
Revised:  The method refines iteratively a sequence of parameter distributions through a combination of local optimisation with partial resampling from a historical prior defined over the support of all previous iterations.
Edit intent: clarity
Original:  We exemplify our method with three biological models using both simulated and real experimental data and retrieve efficiently the parameter values even in the absence of good a priori estimates.
Revised:  We exemplify our method with biological models using both simulated and real experimental data and retrieve efficiently the parameter values even in the absence of good a priori estimates.
Edit intent: clarity
Original:  We exemplify our method with three biological models using both simulated and real experimental data and retrieve efficiently the parameter values even in the absence of good a priori estimates.
Revised:  We exemplify our method with three biological models using both simulated and real experimental data and estimate the parameters efficiently even in the absence of good a priori estimates.
Edit intent: clarity
Original:  The corresponding decision problem is NP-hard, in PSPACE, and SQRT-SUM-hard, hence placing it in NP would imply a breakthrough in long-standing open problems in computer science.
Revised:  The corresponding decision problem is NP-hard, in PSPACE, and SQRT-SUM-hard, hence placing it in NP would imply breakthroughs in long-standing open problems in computer science.
Edit intent: fluency
Original:  Our optimization result establishes that the more general problem of stochastic controller optimization in POMDPs is also NP-hard.
Revised:  Our result establishes that the more general problem of stochastic controller optimization in POMDPs is also NP-hard.
Edit intent: clarity
Original:  To mimick the topology of the cerebral cortex, the network is constructed with local (recurrent) inhibitory connections and distal (feed-forward) excitatory afferents.
Revised:  To mimic the topology of the cerebral cortex, the network is constructed with local (recurrent) inhibitory connections and distal (feed-forward) excitatory afferents.
Edit intent: fluency
Original: I calculate the mean pairwise correlation between neuronsin a network model characterized by strong and random interactions.
Revised: The activity of cortical neurons is correlated, and this correlation affects how the brain processes information. What are the neural circuit mechanisms underlying correlations? Shared synaptic input is necessary to synchronize neurons, but it may not be sufficient if neural circuits are heterogeneous. We study the neural circuit mechanisms of correlations by analyzing a network model characterized by strong and random interactions.
Edit intent: coherence