wanyu/IteraTeR_v2 huggingface dataset:
Original:  By showing that QCC can be solved as a travelling salesman problem, we bridge a theoretical and practical gap between classical circuit design automation and the emerging field of quantum circuit optimisation.
Revised:  Our work bridges a theoretical and practical gap between classical circuit design automation and the emerging field of quantum circuit optimisation.
Edit intent: clarity
Original:  In recent work [ Kilmer and Martin, 2011] , the authors introduced the notion of the t-product, a generalization of matrix multiplication for tensors of order three.
Revised:  In recent work [ Kilmer and Martin, 2011] is a natural generalization of matrix multiplication for tensors of order three.
Edit intent: clarity
Original: In this paper, we study emergent irreducible information in populations of randomly generated computable systems that are networked and follow a "Susceptible-Infected-Susceptible" contagion (or infection) model of imitation of the fittest neighbor.
Revised: In this paper, we study emergent irreducible information in populations of randomly generated computable systems that are networked and follow a "Susceptible-Infected-Susceptible" contagion model of imitation of the fittest neighbor.
Edit intent: coherence
Original:  By making use of its connection to block circulant matrices , the tensor t-function is shown to have similar properties as matrix functions in a number of fundamental scenarios.
Revised:  By making use of its connection to block circulant matrices . The tensor function definition is shown to have similar properties as matrix functions in a number of fundamental scenarios.
Edit intent: clarity
Original:  By making use of its connection to block circulant matrices , the tensor t-function is shown to have similar properties as matrix functions in a number of fundamental scenarios.
Revised:  By making use of its connection to block circulant matrices , the tensor t-function is shown to have similar properties as standard matrix function definitions in fundamental scenarios.
Edit intent: clarity
Original:  In this paper, for any L^p vector space, we show an O(nd)-time solution with a ball of radius O(r) for a fixed \alpha > 1{2}, and for any normed vector space, we show an O(nd)-time solution with a ball of radius O(r) when \alpha > 1{2} as well as an O (nd \log^{(k)}(n))-time solution with a ball of radius O(r) for all \alpha > 0, k \in N, where \log^{(k)}(n) represents the kth iterated logarithm, assuming distance computation and vector space operations take O(d) time.
Revised:  In this paper, for any \ell_p vector space, we show an O(nd)-time solution with a ball of radius O(r) for a fixed \alpha > 1{2}, and for any normed vector space, we show an O(nd)-time solution with a ball of radius O(r) when \alpha > 1{2} as well as an O (nd \log^{(k)}(n))-time solution with a ball of radius O(r) for all \alpha > 0, k \in N, where \log^{(k)}(n) represents the kth iterated logarithm, assuming distance computation and vector space operations take O(d) time.
Edit intent: clarity
Original:  Our methods may be implemented without using Gr\"obner bases;
Revised:  Our methods may be implemented without using Groebner bases;
Edit intent: fluency
Original:  We use it to design a canonization algorithm for general combinatorial objects .
Revised:  We use it to design a canonization algorithm for combinatorial objects in general .
Edit intent: fluency
Original:  We demonstrate the effectiveness and robustness of our method on a wide range of challenging real Internet pictures , and show reconstructed hair sequences from videos.
Revised:  We demonstrate the effectiveness and robustness of our method on a wide range of challenging real Internet pictures and show reconstructed hair sequences from videos.
Edit intent: fluency
Original:  We conclude that the error of BNNs is predominantly caused by the intrinsic instability (training time) and non-robustness (train \& test time).
Revised:  We conclude that the error of BNNs is predominantly caused by the intrinsic instability (training time) and non-robustness (train test time).
Edit intent: fluency
Original: We show  that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is a universal approximator of convex functions.
Revised: We show in this paper that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is a universal approximator of convex functions.
Edit intent: clarity
Original: We show  that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is a universal approximator of convex functions.
Revised: We show that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is an universal approximator of convex functions.
Edit intent: fluency
Original:  The proof uses a dequantization argument from tropical geometry.
Edit intent: coherence
Original:  Under a suitable exponential transformation LSE maps to a family of generalized posynomial functions GPOST, which we also show to be universal approximators for log-log-convex functions.
Revised:  Under a suitable exponential transformation LSE maps to a family of generalized posynomials GPOST, which we also show to be universal approximators for log-log-convex functions.
Edit intent: fluency
Original:  Under a suitable exponential transformation LSE maps to a family of generalized posynomial functions GPOST, which we also show to be universal approximators for log-log-convex functions.
Revised:  Under a suitable exponential transformation LSE maps to a family of generalized posynomial functions GPOST, which we similarly show to be universal approximators for log-log-convex functions.
Edit intent: clarity
Original:  The key feature of interest in the proposed approach is that, once a LSET network is trained on data, the resulting model is convex in the variables, which makes it readily amenable to efficient design based on convex optimization.
Revised:  A key feature of interest in the proposed approach is that, once a LSET network is trained on data, the resulting model is convex in the variables, which makes it readily amenable to efficient design based on convex optimization.
Edit intent: fluency
Original:  The key feature of interest in the proposed approach is that, once a LSET network is trained on data, the resulting model is convex in the variables, which makes it readily amenable to efficient design based on convex optimization.
Revised:  The key feature of an LSET network is that, once a LSET network is trained on data, the resulting model is convex in the variables, which makes it readily amenable to efficient design based on convex optimization.
Edit intent: clarity
Original:  The key feature of interest in the proposed approach is that, once a LSET network is trained on data, the resulting model is convex in the variables, which makes it readily amenable to efficient design based on convex optimization.
Revised:  The key feature of interest in the proposed approach is that, once it is trained on data, the resulting model is convex in the variables, which makes it readily amenable to efficient design based on convex optimization.
Edit intent: clarity
Original:  Similarly, once a GPOST model is trained on data, it yields a posynomial model that can be efficiently optimized with respect to its variables by using Geometric Programming (GP).
Revised:  Similarly, once a GPOST model is trained on data, it yields a posynomial model that can be efficiently optimized with respect to its variables by using geometric programming (GP).
Edit intent: fluency
Original:  Many relevant phenomena in physics and engineering can indeed be modeled, either exactly or approximately, via convex or log-log-convex models.
Edit intent: coherence
Original:  The proposed methodology is illustrated by two numerical examples in which LSET and GPOST models are used to first approximate data gathered from the simulations of two physical processes ( the vibration from a vehicle suspension system, and the peak power generated by the combustion of propane), and to later optimize these models.
Revised:  The proposed methodology is illustrated by two numerical examples , in which, first, models are constructed from simulation data of the two physical processes ( the vibration from a vehicle suspension system, and the peak power generated by the combustion of propane), and to later optimize these models.
Edit intent: clarity
Original:  The proposed methodology is illustrated by two numerical examples in which LSET and GPOST models are used to first approximate data gathered from the simulations of two physical processes ( the vibration from a vehicle suspension system, and the peak power generated by the combustion of propane), and to later optimize these models.
Revised:  The proposed methodology is illustrated by two numerical examples in which LSET and GPOST models are used to first approximate data gathered from the simulations of two physical processes ( namely, the level of vibration in a vehicle suspension system, and the peak power generated by the combustion of propane), and to later optimize these models.
Edit intent: clarity
Original:  The proposed methodology is illustrated by two numerical examples in which LSET and GPOST models are used to first approximate data gathered from the simulations of two physical processes ( the vibration from a vehicle suspension system, and the peak power generated by the combustion of propane), and to later optimize these models.
Revised:  The proposed methodology is illustrated by two numerical examples in which LSET and GPOST models are used to first approximate data gathered from the simulations of two physical processes ( the vibration from a vehicle suspension system, and the peak power generated by the combustion of propane), and then optimization-based design is performed on these models.
Edit intent: clarity
Original: The ability to integrate information into a unified coherent whole is a fundamental capacity of many biological and cognitive systems.
Revised: The capacity to integrate information into a unified coherent whole is a fundamental capacity of many biological and cognitive systems.
Edit intent: fluency
Original: The ability to integrate information into a unified coherent whole is a fundamental capacity of many biological and cognitive systems.
Revised: The ability to integrate information is a prominent feature of biological and cognitive systems.
Edit intent: clarity
Original:  We argue that modelling and understanding how measures of information integration operate in these scenarios is fundamental to adequately capture integration in systems such as the brain.
Revised:  Here, we show for the first time how measures of information integration operate in these scenarios is fundamental to adequately capture integration in systems such as the brain.
Edit intent: clarity
Original:  We propose a simplified and modified version of integrated information \phi%DIFDELCMD < } %%% in order to explore these questions.
Revised:  We propose a simplified and modified version of integrated information %DIFDELCMD < } %%% in order to explore these questions.
Edit intent: fluency
Original:  Using mean field approximations, we measure \phi%DIFDELCMD < } %%% in a kinetic Ising models of infinite size.
Revised:  Using mean field approximations, we measure %DIFDELCMD < } %%% in a kinetic Ising models of infinite size.
Edit intent: coherence
Original:  Moreover, we find that we can delimit the boundary of a system with respect to its environment by comparing the divergent integrative tendencies of system and system-environment processes respectively .
Revised:  Moreover, by comparing different divergent tendencies of blocks of a system at these critical points, we delimit the boundary between an integrated unit and its environment .
Edit intent: clarity
Original:  Finally, we model a system that maintains integrated information when interacting with a range of different environments by generating a critical surface spanning a parametric region of the environment.
Revised:  Finally, we present a model that adaptively maintains its integration despite changes in its environment by generating a critical surface spanning a parametric region of the environment.
Edit intent: clarity
Original:  Here we develop a Bayesian reconstruction approach that lifts these limitations by not only allowing for heterogeneous errors, but also for individual edge measurements without direct error estimates.
Revised:  Here we develop a Bayesian reconstruction approach that lifts these limitations by not only allowing for heterogeneous errors, but also for single edge measurements without direct error estimates.
Edit intent: clarity
Original:  Our approach works by coupling the inference approach with structured generative network models, which enable the correlations between edges to be used as reliable error estimates.
Revised:  Our approach works by coupling the inference approach with structured generative network models, which enable the correlations between edges to be used as reliable uncertainty estimates.
Edit intent: clarity
Original:  We show the robustness of our approach compared to state-of-the art algorithms in detecting disparate (shared and private) communities on synthetic data as well as on real genome-wide fibroblast proliferation dataset.
Revised:  We show that our approach outperforms state-of-the-art algorithms in detecting disparate (shared and private) communities on synthetic data as well as on real genome-wide fibroblast proliferation dataset.
Edit intent: clarity
Original: In this chapter, we explore how (Type-2) computable distributions can be used to give both distributional and (algorithmic) sampling  semantics to probabilistic programs with continuous distributions.
Revised: In this chapter, we explore how (Type-2) computable distributions can be used to give both (algorithmic) sampling semantics to probabilistic programs with continuous distributions.
Edit intent: clarity
Original:  Towards this end, we first sketch an encoding of computable distributions in a fragment of Haskell . Next, we show how topological domains can be used to model the resulting PCF-like language.
Revised:  Towards this end, we sketch an encoding of computable distributions in a fragment of Haskell . Next, we show how topological domains can be used to model the resulting PCF-like language.
Edit intent: coherence
Original:  Towards this end, we first sketch an encoding of computable distributions in a fragment of Haskell . Next, we show how topological domains can be used to model the resulting PCF-like language.
Revised:  Towards this end, we first sketch an encoding of computable distributions in a fragment of Haskell and show how topological domains can be used to model the resulting PCF-like language.
Edit intent: coherence
Original: We derive new results related to the portfolio choice problem for a power and logarithmic utilities.
Revised: We derive new results related to the portfolio choice problem for power and logarithmic utilities.
Edit intent: fluency
Original:  Assuming that the portfolio returns follow a log-normal distribution, the closed-form expressions of the optimal portfolio weights are obtained for both utility functions.
Revised:  Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio weights are obtained for both utility functions.
Edit intent: clarity
Original:  [STOC'16] recently studied the query and round complexity of classic and popu- lar   problems such as finding the maximum ( max ), finding all elements above a certain value ( threshold-v ) or computing the top-k elements of an array (top-k ) in a noisy environment.
Revised:  [STOC'16] studied the problems such as finding the maximum ( max ), finding all elements above a certain value ( threshold-v ) or computing the top-k elements of an array (top-k ) in a noisy environment.
Edit intent: coherence
Original:  [STOC'16] recently studied the query and round complexity of classic and popu- lar   problems such as finding the maximum ( max ), finding all elements above a certain value ( threshold-v ) or computing the top-k elements of an array (top-k ) in a noisy environment.
Revised:  [STOC'16] recently studied the query and round complexity of classic and popu- lar round problems such as finding the maximum ( max ), finding all elements above a certain value ( threshold-v ) or computing the top-k elements of an array (top-k ) in a noisy environment.
Edit intent: fluency
Original:  [STOC'16] recently studied the query and round complexity of classic and popu- lar   problems such as finding the maximum ( max ), finding all elements above a certain value ( threshold-v ) or computing the top-k elements of an array (top-k ) in a noisy environment.
Revised:  [STOC'16] recently studied the query and round complexity of classic and popu- lar problems such as finding the maximum ( max ), finding all elements above a certain value ( threshold-v ) or computing the top-k elements of an array (top-k ) in a noisy environment.
Edit intent: fluency
Original:  [STOC'16] recently studied the query and round complexity of classic and popu- lar   problems such as finding the maximum ( max ), finding all elements above a certain value ( threshold-v ) or computing the top-k elements of an array (top-k ) in a noisy environment.
Revised:  [STOC'16] recently studied the query and round complexity of classic and popu- lar problems such as finding the maximum ( max ), finding all elements above a certain value ( threshold-v ) or computing the top-k elements ( ) in a noisy environment.
Edit intent: clarity
Original:  [STOC'16] recently studied the query and round complexity of classic and popu- lar   problems such as finding the maximum ( max ), finding all elements above a certain value ( threshold-v ) or computing the top-k elements of an array (top-k ) in a noisy environment.
Revised:  [STOC'16] recently studied the query and round complexity of classic and popu- lar problems such as finding the maximum ( max ), finding all elements above a certain value ( threshold-v ) or computing the top-k elements of an array (top-k-k ) in a noisy environment.
Edit intent: fluency
Original:  An illustrating exampleis the task of selecting papers for a conference.
Revised:  For example, consider the task of selecting papers for a conference.
Edit intent: clarity
Original:  This task is challenging due the crowdsourcing-nature of peer reviews: (1) the results of reviews are noisy and (2) it is necessary to parallelize the review process as much as possible.
Revised:  This task is challenging due the crowdsourcing nature of peer reviews: (1) the results of reviews are noisy and (2) it is necessary to parallelize the review process as much as possible.
Edit intent: fluency
Original:  This task is challenging due the crowdsourcing-nature of peer reviews: (1) the results of reviews are noisy and (2) it is necessary to parallelize the review process as much as possible.
Revised:  This task is challenging due the crowdsourcing-nature of peer reviews: the results of reviews are noisy and (2) it is necessary to parallelize the review process as much as possible.
Edit intent: fluency
Original:  This task is challenging due the crowdsourcing-nature of peer reviews: (1) the results of reviews are noisy and (2) it is necessary to parallelize the review process as much as possible.
Revised:  This task is challenging due the crowdsourcing-nature of peer reviews: (1) the results of reviews are noisy and it is necessary to parallelize the review process as much as possible.
Edit intent: coherence
Original:  Thus, we study these fundamental problems in the noisy value model and the noisy comparison model: In the noisy value model, every review returns a value (e.g. \emph{ \eg accept).
Revised:  We study the noisy value model and the noisy comparison model: In the noisy value model, every review returns a value (e.g. \emph{ \eg accept).
Edit intent: clarity
Original:  Thus, we study these fundamental problems in the noisy value model and the noisy comparison model: In the noisy value model, every review returns a value (e.g. \emph{ \eg accept).
Revised:  Thus, we study these fundamental problems in the noisy value model and the noisy comparison model: In the \emph{ \eg accept).
Edit intent: coherence
Original:  Thus, we study these fundamental problems in the noisy value model and the noisy comparison model: In the noisy value model, every review returns a value (e.g. \emph{ \eg accept).
Revised:  Thus, we study these fundamental problems in the noisy value model and the noisy comparison model: In the noisy value model, every review returns a value (e.g. \emph{noisy value model \eg accept).
Edit intent: clarity
Original:  In the noisy comparison model \emph{ (introduced in the seminal work of Feige et al.
Revised:  In the \emph{ (introduced in the seminal work of Feige et al.
Edit intent: clarity
Original:  In the noisy comparison model \emph{ (introduced in the seminal work of Feige et al.
Revised:  In the noisy comparison model \emph{noisy comparison model (introduced in the seminal work of Feige et al.
Edit intent: fluency
Original:  In a first step , we show optimal worst-case \textsc{ \textsc{ \textsc{ \textsc{ \textsc{  upper and lower bounds on the round vs query complexity for max and top-k in all models.
Revised:  In this paper , we show optimal worst-case \textsc{ \textsc{ \textsc{ \textsc{ \textsc{ upper and lower bounds on the round vs query complexity for max and top-k in all models.
Edit intent: clarity
Original:  In a first step , we show optimal worst-case \textsc{ \textsc{ \textsc{ \textsc{ \textsc{  upper and lower bounds on the round vs query complexity for max and top-k in all models.
Revised:  In a first step , we show optimal worst-case \textsc{ ,\textsc{ \textsc{ \textsc{ \textsc{ upper and lower bounds on the round vs query complexity for max and top-k in all models.
Edit intent: fluency
Original:  In a first step , we show optimal worst-case \textsc{ \textsc{ \textsc{ \textsc{ \textsc{  upper and lower bounds on the round vs query complexity for max and top-k in all models.
Revised:  In a first step , we show optimal worst-case \textsc{ \textsc{ \textsc{Top \textsc{ \textsc{ upper and lower bounds on the round vs query complexity for max and top-k in all models.
Edit intent: fluency
Original:  In a first step , we show optimal worst-case \textsc{ \textsc{ \textsc{ \textsc{ \textsc{  upper and lower bounds on the round vs query complexity for max and top-k in all models.
Revised:  In a first step , we show optimal worst-case \textsc{ \textsc{ \textsc{ \textsc{ and\textsc{ upper and lower bounds on the round vs query complexity for max and top-k in all models.
Edit intent: coherence
Original:  For threshold-v \textsc{  , we obtain optimal query complexity and nearly-optimal (i.e., optimal up to a factor O(log log k), where k is the size of the output) round complexity for all models.
Revised:  For threshold-v \textsc{ , we obtain optimal query complexity and nearly-optimal round complexity, where k is the size of the output) round complexity for all models.
Edit intent: clarity
Original:  For threshold-v \textsc{  , we obtain optimal query complexity and nearly-optimal (i.e., optimal up to a factor O(log log k), where k is the size of the output) round complexity for all models.
Revised:  For threshold-v \textsc{ , we obtain optimal query complexity and nearly-optimal (i.e., optimal up to a factor O(log log k), where k is the size of the output) for both models.
Edit intent: clarity