wanyu/IteraTeR_v2 huggingface dataset:
Original:  Here we shed new light on QT by having it follow from two main postulates (i) the theory should be logically consistent;
Revised:  Here we shed new light on QT by being based on two main postulates (i) the theory should be logically consistent;
Edit intent: clarity
Original:  Here we shed new light on QT by having it follow from two main postulates (i) the theory should be logically consistent;
Revised:  Here we shed new light on QT by having it follow from two main postulates : 1. the theory should be logically consistent;
Edit intent: clarity
Original:  (ii) inferences in the theory should be computable in polynomial time.
Revised:  2. inferences in the theory should be computable in polynomial time.
Edit intent: coherence
Original: The idea of equivariance to symmetry transformations provides one of the first theoretically grounded principles for neural network architecture design.
Revised: The principle of equivariance to symmetry transformations provides one of the first theoretically grounded principles for neural network architecture design.
Edit intent: clarity
Original: The idea of equivariance to symmetry transformations provides one of the first theoretically grounded principles for neural network architecture design.
Revised: The idea of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design.
Edit intent: clarity
Original:  Here we show how this principle can be extended beyond global symmetries to local gauge transformations , thereby enabling the development of equivariant convolutional networks on general manifolds .
Revised:  Here we show how this principle can be extended beyond global symmetries to local gauge transformations . This enables the development of equivariant convolutional networks on general manifolds .
Edit intent: coherence
Original:  We implement gauge equivariant CNNs for signals defined on the  icosahedron, which provides a reasonable approximation of spherical signals .
Revised:  We implement gauge equivariant CNNs for signals defined on the surface of the icosahedron, which provides a reasonable approximation of spherical signals .
Edit intent: clarity
Original:  We implement gauge equivariant CNNs for signals defined on the  icosahedron, which provides a reasonable approximation of spherical signals .
Revised:  We implement gauge equivariant CNNs for signals defined on the icosahedron, which provides a reasonable approximation of the sphere .
Edit intent: fluency
Original:  We evaluate the Icosahedral CNN on omnidirectional image segmentation and climate pattern segmentation, and find that it outperforms previous methods .
Revised:  Using this method, we demonstrate substantial improvements over previous methods on the task of segmenting omnidirectional images and global climate patterns .
Edit intent: clarity
Original:  In this paper, we introduce delayed-action games (DAGs) formalism that simulates hidden-information games (HIGs) as SMGs, by eliminating hidden information by delaying a player's actions.
Revised:  In this paper, we introduce delayed-action games (DAGs) formalism that simulates hidden-information games (HIGs) as SMGs, where hidden information is captured by delaying a player's actions.
Edit intent: clarity
Original:  The elimination of hidden information enables the usage of SMG off-the-shelf model checkers to implement HIGs.
Revised:  The elimination of private variables enables the usage of SMG off-the-shelf model checkers to implement HIGs.
Edit intent: clarity
Original:  Since each subgame can be independently explored, parallel computation can be utilized to reduce the model checking time, while alleviating the state space explosion problem that SMGs are notorious for.
Revised:  Since each subgame can be independently explored, utilizing parallel computation to reduce the model checking time, while alleviating the state space explosion problem that SMGs are notorious for.
Edit intent: fluency
Original:  Finally, we demonstrate applicability of the DAG-based synthesis framework on a case study of a human-on-the-loop unmanned-aerial vehicle system that may be under stealthy attack , where the proposed framework is used to formally model, analyze and synthesize security-aware strategies for the system.
Revised:  Finally, we demonstrate applicability of the DAG-based synthesis framework on a case study of a human-on-the-loop unmanned-aerial vehicle system under stealthy attacks , where the proposed framework is used to formally model, analyze and synthesize security-aware strategies for the system.
Edit intent: coherence
Original: In this paper we propose a systematic approach for calculating the preserved measures and integrals of a rational map .
Revised: In this paper we propose a systematic approach for calculating the preserved measures and integrals of rational maps .
Edit intent: fluency
Original:  Given sufficient computing power, all rational preserved integrals can be found  .
Revised:  Given sufficient computing power, most, if not all, rational preserved integrals can be found .
Edit intent: clarity
Original: Although the performance of base-line Evolutionary Algorithms (EAs) on linear functions has been studied rigorously , the same theoretical analyses on non-linear objectives are still far behind.
Revised: The performance of base-line Evolutionary Algorithms (EAs) on linear functions has been studied rigorously , the same theoretical analyses on non-linear objectives are still far behind.
Edit intent: coherence
Original: Although the performance of base-line Evolutionary Algorithms (EAs) on linear functions has been studied rigorously , the same theoretical analyses on non-linear objectives are still far behind.
Revised: Although the performance of base-line Evolutionary Algorithms (EAs) on linear functions has been studied rigorously , the same theoretical analyses on non-linear problems is still far behind.
Edit intent: clarity
Original:  In this paper, variations of the Packing While Travelling (PWT) , also known as a non-linear knapsack problem , is considered to address this gap .
Revised:  In this paper, variations of the Packing While Travelling (PWT) -- also known as a non-linear knapsack problem , is considered to address this gap .
Edit intent: fluency
Original:  In this paper, variations of the Packing While Travelling (PWT) , also known as a non-linear knapsack problem , is considered to address this gap .
Revised:  In this paper, variations of the Packing While Travelling (PWT) , also known as the non-linear knapsack problem , is considered to address this gap .
Edit intent: fluency
Original:  We investigate PWT for two cities  with correlated weights and profits  using single-objective and multi-objective algorithms.
Revised:  We investigate PWT for two cities with correlated weights and profits , using single-objective and multi-objective algorithms.
Edit intent: fluency
Original:  Our results show that RLS  finds the optimal solution in O(n^3) expected time while the GSEMO enhanced with a specific selection operator to deal with exponential population size, calculates all the Pareto front solutions in the same  expected time.
Revised:  Our results show that RLS finds the optimal solution in O(n^3) expected time while the GSEMO enhanced with a specific selection operator to deal with exponential population size, and prove that it finds the Pareto front solutions in the same expected time.
Edit intent: coherence
Original:  Our results show that RLS  finds the optimal solution in O(n^3) expected time while the GSEMO enhanced with a specific selection operator to deal with exponential population size, calculates all the Pareto front solutions in the same  expected time.
Revised:  Our results show that RLS finds the optimal solution in O(n^3) expected time while the GSEMO enhanced with a specific selection operator to deal with exponential population size, calculates all the Pareto front in the same expected time.
Edit intent: fluency
Original:  In the case of uniform weights, (1+1)~EA is able to find the optimal solution in expected time O(n^2 \log{(\max\{n,p_{max\})}} \})}} ), where p_{ max } is the largest profit of the given items.
Revised:  In the case of uniform weights, (1+1)~EA is able to find the optimal solution in expected time O(n^2 \log{(\max\{n,p_{max\})}} \log{(\max\{n,p_{\max\})}} ), where p_{ max } is the largest profit of the given items.
Edit intent: fluency
Original:  In the case of uniform weights, (1+1)~EA is able to find the optimal solution in expected time O(n^2 \log{(\max\{n,p_{max\})}} \})}} ), where p_{ max } is the largest profit of the given items.
Revised:  In the case of uniform weights, (1+1)~EA is able to find the optimal solution in expected time O(n^2 \log{(\max\{n,p_{max\})}} \})}} ), where p_{ \max } is the largest profit of the given items.
Edit intent: fluency
Original:  We also validate the theoretical results using practical experiments and present estimation for expected running time according to the experiments .
Revised:  We also perform an experimental analysis to complement our theoretical investigations and provide additional insights into the runtime behavior .
Edit intent: clarity
Original: In a social network the individuals or nodes connect to other nodes by choosing one of the channels of communication at a time to re-establish the existing social links.
Revised: In a social network individuals or nodes connect to other nodes by choosing one of the channels of communication at a time to re-establish the existing social links.
Edit intent: clarity
Original:  Since information for research is usually restricted to a limited number of channels or layers, these autonomous decision making processes by the nodes constitute the sampling of a multiplex network leading to just one (though very important) example of sampling bias caused by the behavior of the nodes.
Revised:  Since available data sets are usually restricted to a limited number of channels or layers, these autonomous decision making processes by the nodes constitute the sampling of a multiplex network leading to just one (though very important) example of sampling bias caused by the behavior of the nodes.
Edit intent: clarity
Original:  Assuming that the nodal attributes are independently drawn from an arbitrary distribution \rho(h) and that the sampling probability r(h_i , h_j) for a link ij of nodal attributes h_i and h_j is also arbitrary, we are able to derive exact analytic expressions of the sampled network for such network characteristics as the degree distribution, degree correlation, and clustering spectrum.
Revised:  Assuming that the nodal attributes are independently drawn from an arbitrary distribution \rho(h) and that the sampling probability r(h_i , h_j) for a link ij of nodal attributes h_i and h_j is also arbitrary, we derive exact analytic expressions of the sampled network for such network characteristics as the degree distribution, degree correlation, and clustering spectrum.
Edit intent: clarity
Original:  For arbitrary measurements, we also show that practical recovery could be achieved  when m \asymp r s  \ln(en/s) via an iterative-hard-thresholding algorithm provided one could answer positively a question ] about head projections for the jointly low-rank and bisparse structure.
Revised:  In case of arbitrary measurements, we also show that practical recovery could be achieved when m \asymp r s \ln(en/s) via an iterative-hard-thresholding algorithm provided one could answer positively a question ] about head projections for the jointly low-rank and bisparse structure.
Edit intent: clarity
Original:  For arbitrary measurements, we also show that practical recovery could be achieved  when m \asymp r s  \ln(en/s) via an iterative-hard-thresholding algorithm provided one could answer positively a question ] about head projections for the jointly low-rank and bisparse structure.
Revised:  For arbitrary measurements, we also show that practical recovery could be achieved via an iterative-hard-thresholding algorithm when m \asymp r s \ln(en/s) via an iterative-hard-thresholding algorithm provided one could answer positively a question ] about head projections for the jointly low-rank and bisparse structure.
Edit intent: fluency
Original:  In case of arbitrary measurements, we also show that practical recovery could be achieved via an iterative-hard-thresholding algorithm when m \asymp r s^\gamma \ln(en/s) for some exponent \gamma  \in [1,2] . Its precise value is the object of a question, raised but unresolved in this paper, about head projections for the jointly low-rank and bisparse structure.
Revised:  In case of arbitrary measurements, we investigate the possibility of achieving practical recovery via an iterative-hard-thresholding algorithm when m \asymp r s^\gamma \ln(en/s) for some exponent \gamma \in [1,2] . Its precise value is the object of a question, raised but unresolved in this paper, about head projections for the jointly low-rank and bisparse structure.
Edit intent: clarity
Original:  In case of arbitrary measurements, we also show that practical recovery could be achieved via an iterative-hard-thresholding algorithm when m \asymp r s^\gamma \ln(en/s) for some exponent \gamma  \in [1,2] . Its precise value is the object of a question, raised but unresolved in this paper, about head projections for the jointly low-rank and bisparse structure.
Revised:  In case of arbitrary measurements, we also show that practical recovery could be achieved via an iterative-hard-thresholding algorithm when m \asymp r s^\gamma \ln(en/s) for some exponent \gamma \in [1,2] is the object of a question, raised but unresolved in this paper, about head projections for the jointly low-rank and bisparse structure.
Edit intent: clarity
Original:  For the rank-one measurements, we suggest on arcane grounds an iterative-hard-thresholding algorithm modified to exploit the nonstandard restricted isometry property obeyed by this type of measurements.
Revised:  For rank-one measurements, we suggest on arcane grounds an iterative-hard-thresholding algorithm modified to exploit the nonstandard restricted isometry property obeyed by this type of measurements.
Edit intent: fluency
Original:  Previous approach develops a nice relational program logic framework for  expected sensitivity of probabilistic while loops, where the number of iterations is fixed and bounded.
Revised:  A previous approach develops a nice relational program logic framework for expected sensitivity of probabilistic while loops, where the number of iterations is fixed and bounded.
Edit intent: coherence
Original:  Previous approach develops a nice relational program logic framework for  expected sensitivity of probabilistic while loops, where the number of iterations is fixed and bounded.
Revised:  Previous approach develops a nice relational program logic framework for proving expected sensitivity of probabilistic while loops, where the number of iterations is fixed and bounded.
Edit intent: coherence
Original:  In this work we present a sound approach for sensitivity analysis of probabilistic while loops , where the number of iterations is not fixed, but is randomized and only the expected number of iterations is finite.
Revised:  In this work , we consider probabilistic while loops , where the number of iterations is not fixed, but is randomized and only the expected number of iterations is finite.
Edit intent: clarity
Original:  In this work we present a sound approach for sensitivity analysis of probabilistic while loops , where the number of iterations is not fixed, but is randomized and only the expected number of iterations is finite.
Revised:  In this work we present a sound approach for sensitivity analysis of probabilistic while loops where the number of iterations is not fixed, but is randomized and only the expected number of iterations is finite.
Edit intent: fluency
Original:  A previous approach develops a nice relational program logic framework for proving expected sensitivity of probabilistic while loops, where the number of iterations is fixed and bounded.
Revised:  A previous approach develops a relational program logic framework for proving expected sensitivity of probabilistic while loops, where the number of iterations is fixed and bounded.
Edit intent: clarity
Original: Finite element methods (FEM) are widely used for bounded heterogeneous media models, and boundary element methods (BEM) are efficient for simulating wave propagation in unbounded homogeneous media.
Edit intent: coherence
Original:  A natural medium for wave propagation comprises a coupled bounded heterogeneous region and an unbounded homogeneous free space .
Revised:  A natural medium for wave propagation comprises a coupled bounded heterogeneous region and an unbounded homogeneous free-space .
Edit intent: fluency
Original:  It is desirable to develop algorithms that incorporate the full physics of the heterogenous and unbounded medium wave propagation model, and avoid  approximation of the RC.
Revised:  It is desirable to develop algorithms that incorporate the full physics of the heterogeneous and unbounded medium wave propagation model, and avoid approximation of the RC.
Edit intent: fluency
Original:  It is desirable to develop algorithms that incorporate the full physics of the heterogenous and unbounded medium wave propagation model, and avoid  approximation of the RC.
Revised:  It is desirable to develop algorithms that incorporate the full physics of the heterogenous and unbounded medium wave propagation model, and avoid an approximation of the RC.
Edit intent: fluency
Original:  Consequently we develop a novel overlapping FEM-BEM algorithm to simulate the equivalent coupled heterogeneous and unbounded medium system , modeling acoustic or electromagnetic wave propagation in two dimensions.
Revised:  Consequently we develop a novel overlapping FEM-BEM algorithm for simulating the acoustic or electromagnetic wave propagation in two dimensions.
Edit intent: clarity
Original:  Our numerical experiments demonstrate efficiency of the FEM-BEM framework, for models with heterogeneous media comprising smooth and complex non-smooth regions .
Revised:  Our numerical experiments demonstrate efficiency of the FEM-BEM approach for simulating smooth and non-smooth regions .
Edit intent: clarity
Original:  In this paper, we investigate the BCD method for solving linear and non-linear ill-posed inverse problems.
Revised:  In this paper, we investigate the BCD method for solving linear inverse problems.
Edit intent: coherence
Original:  To understand whether fission yeast uses a mix of sizer and adder control, or whether size sensing is simply imprecise, we developed a mathematical model of sizer control , including the relevant sources of variation.
Revised:  Here we investigate possible reasons for this discrepancy by developing a mathematical model of sizer control , including the relevant sources of variation.
Edit intent: clarity
Original:  These findings demonstrate that refined analysis of geometric variation can lead to new insights into cell size control.
Revised:  These findings demonstrate that analysis of geometric variation can lead to new insights into cell size control.
Edit intent: clarity
Original: Convection schemes are a large source of error in global weather and climate models, and modern resolutions are often too fine to parameterize convection but are still too coarse to fully resolve it.
Revised: Convection schemes are a large source of error in global weather and climate models, and modern resolutions are often too fine to parameterise convection but are still too coarse to fully resolve it.
Edit intent: fluency
Original:  The technique involves splitting the atmosphere into various fluid components which are defined by their physical properties, such as the stable environment or buoyant updrafts .
Revised:  The technique involves splitting the atmosphere into multiple fluids. For example, the atmosphere could be divided into buoyant updrafts and stable regions .
Edit intent: clarity
Original:  Relatively little is known about the numerical stability of the multi-fluid equations or the numerical properties of mass transfer terms between the fluids.
Revised:  Relatively little is known about the numerical properties of mass transfer terms between the fluids.
Edit intent: clarity
Original:  2. We derive mass transfer terms which relabel the fluids and derive numerical properties of the transfer schemes  including boundedness, momentum conservation and energy properties . Numerical solutions of the multi-fluid Euler equations  are presented using stable and unstable treatments of the transfers  .
Revised:  2. We derive mass transfer terms which relabel the fluids and derive numerical properties of the transfer schemes , including boundedness, momentum conservation and energy properties . Numerical solutions of the multi-fluid Euler equations are presented using stable and unstable treatments of the transfers .
Edit intent: fluency
Original:  2. We derive mass transfer terms which relabel the fluids and derive numerical properties of the transfer schemes  including boundedness, momentum conservation and energy properties . Numerical solutions of the multi-fluid Euler equations  are presented using stable and unstable treatments of the transfers  .
Revised:  2. We derive mass transfer terms which relabel the fluids and derive numerical properties of the transfer schemes including boundedness, momentum conservation and energy conservation . Numerical solutions of the multi-fluid Euler equations are presented using stable and unstable treatments of the transfers .
Edit intent: fluency
Original: Recently several algorithms based on Empirical Mode Decomposition (EMD) have been proposed to decompose two or higher dimensional nonstationary signals which are varying over time, like the Bivariate, Multivariate EMD and Noise-Assisted Multivariate EMD.
Edit intent: coherence
Original:  In this work we present a new method called Multivariate Fast Iterative Filtering ( MFIF) , which is based on the recently proposed Fast Iterative Filtering technique, able to decompose uniquely these kind of signals in a fast and stable way.
Revised:  In this work we propose an extension of the Fast Iterative Filtering ( MFIF) , which is based on the recently proposed Fast Iterative Filtering technique, able to decompose uniquely these kind of signals in a fast and stable way.
Edit intent: clarity
Original:  Finally, we compare its performance with the one of the main methods developed so far in the literature, proving that MvFIF produces in a really fast and reliable manner, and without any a priori assumption on the signal under investigation , a unique decomposition of any multivariate signal.
Revised:  Finally, we compare its performance with the one of the main methods developed so far in the literature, proving that MvFIF produces , without any a priori assumption on the signal under investigation , a unique decomposition of any multivariate signal.
Edit intent: coherence
Original:  Finally, we compare its performance with the one of the main methods developed so far in the literature, proving that MvFIF produces in a really fast and reliable manner, and without any a priori assumption on the signal under investigation , a unique decomposition of any multivariate signal.
Revised:  Finally, we compare its performance with the one of the main methods developed so far in the literature, proving that MvFIF produces in a really fast and reliable manner, and without any a priori assumption on the signal under investigation and in a fast and reliable manner, a uniquely defined decomposition of any multivariate signal.
Edit intent: clarity
Original:  However, there are many more other challenges at different levels, e.g., item feature level and session level, and from various perspectives, e.g., item heterogeneity and intra- and inter-item feature coupling relations, associated with SBRS.
Revised:  However, there are many more other challenges at different levels, e.g., sessions), behaviors ( e.g., item heterogeneity and intra- and inter-item feature coupling relations, associated with SBRS.
Edit intent: clarity