wanyu/IteraTeR_v2 huggingface dataset:
Original:  In the current paper we show how to analytically derive weighting functions to realise arbitrary spectra which are isotropic and solenoidal using a superposition of weighted Gaussian spectra of differing length scales.
Revised:  In the current paper we show how to analytically derive weighting functions to realise arbitrary spectra which are isotropic and solenoidal using a superposition of weighted Gaussian spectra of different length scales.
Edit intent: fluency
Original:  The analytic weighting functions for the von Karman , the Liepmann, and the modified von Karman spectra are derived subsequently.
Revised:  The analytic weighting functions for the von K\'arm\'an , the Liepmann, and the modified von Karman spectra are derived subsequently.
Edit intent: fluency
Original:  The analytic weighting functions for the von Karman , the Liepmann, and the modified von Karman spectra are derived subsequently.
Revised:  The analytic weighting functions for the von Karman , the Liepmann, and the modified von K\'arm\'an spectra are derived subsequently.
Edit intent: fluency
Original:  Finally it is shown how to discretise the weighting functions to use a limited number of Gaussian spectra only .
Revised:  Finally a method is proposed to discretise the weighting functions to use a limited number of Gaussian spectra only .
Edit intent: clarity
Original:  Finally it is shown how to discretise the weighting functions to use a limited number of Gaussian spectra only .
Revised:  Finally it is shown how to discretise the problem using a limited number of Gaussian spectra only .
Edit intent: clarity
Original:  Finally it is shown how to discretise the weighting functions to use a limited number of Gaussian spectra only .
Revised:  Finally it is shown how to discretise the weighting functions to use a limited number of Gaussian spectra .
Edit intent: clarity
Original:  The effectivity of the discrete method is demonstrated by realising a von Karman velocity spectrum using the RPM method.
Revised:  The effectivity of this approach is demonstrated by realising a von Karman velocity spectrum using the RPM method.
Edit intent: clarity
Original:  The effectivity of the discrete method is demonstrated by realising a von Karman velocity spectrum using the RPM method.
Revised:  The effectivity of the discrete method is demonstrated by realising a von K\'arm\'an velocity spectrum using the RPM method.
Edit intent: fluency
Original: The Dubins Traveling Salesman Problem (DTSP) has received significant interest over the last decade due to its occurrence in several civil and military surveillance applications.
Revised: The Dubins Traveling Salesman Problem (DTSP) has generated significant interest over the last decade due to its occurrence in several civil and military surveillance applications.
Edit intent: clarity
Original:  However, in many problem instances, this lower bound computed by solving the ETSP is far away from the cost of the feasible solutions obtained by some well known algorithms for the DTSP.
Revised:  However, in many problem instances, the lower bound computed by solving the ETSP is far away from the cost of the feasible solutions obtained by some well known algorithms for the DTSP.
Edit intent: coherence
Original:  However, in many problem instances, this lower bound computed by solving the ETSP is far away from the cost of the feasible solutions obtained by some well known algorithms for the DTSP.
Revised:  However, in many problem instances, this lower bound computed by solving the ETSP is far below the cost of the feasible solutions obtained by some well known algorithms for the DTSP.
Edit intent: clarity
Original:  However, in many problem instances, this lower bound computed by solving the ETSP is far away from the cost of the feasible solutions obtained by some well known algorithms for the DTSP.
Revised:  However, in many problem instances, this lower bound computed by solving the ETSP is far away from the cost of the feasible solutions obtained by some well-known algorithms for the DTSP.
Edit intent: fluency
Original:  This article addresses this fundamental issue and presents the first systematic procedure with computational results for developing tight lower bounds for the DTSP.
Revised:  This article addresses this fundamental issue and presents the first systematic procedure for developing tight lower bounds for the DTSP.
Edit intent: clarity
Original:  As usual, applications that use these databases  evolve over time, sometimes necessitating (or preferring) a change to the format  of the data.
Revised:  Applications that use these databases evolve over time, sometimes necessitating (or preferring) a change to the format of the data.
Edit intent: coherence
Original:  As usual, applications that use these databases  evolve over time, sometimes necessitating (or preferring) a change to the format  of the data.
Revised:  As usual, applications that use these databases will evolve over time, sometimes necessitating (or preferring) a change to the format of the data.
Edit intent: clarity
Original:  As usual, applications that use these databases  evolve over time, sometimes necessitating (or preferring) a change to the format  of the data.
Revised:  As usual, applications that use these databases evolve over time, sometimes necessitating (or preferring) a change to the format or organization of the data.
Edit intent: clarity
Original:  The problem we address in this paper is: How can we support the evolution of high-availability applications and their NoSQL data on-line , without excessive delays or interruptions ?
Revised:  The problem we address in this paper is: How can we support the evolution of high-availability applications and their NoSQL data online , without excessive delays or interruptions ?
Edit intent: fluency
Original:  This requires orchestrating the changes among the database and all the clients accessing it, and is challenging to implement in a safe and general-purpose manner in the presence of backward-incompatible data-format changes.
Revised:  This requires orchestrating the changes among the database and all the clients accessing it, and is challenging to implement in a safe and general-purpose manner in the presence of backward-incompatible data- format changes?
Edit intent: fluency
Original:  KVolve permits a developer to submit an upgrade specification ,written in a domain-specific language we developed that define show to transform existing data to the newest version.
Revised:  KVolve permits a developer to submit an upgrade specification that defines how to transform existing data to the newest version.
Edit intent: coherence
Original:  This transformation is applied lazily , as applications interact with the database, thus avoiding long pause times.
Revised:  This transformation is applied lazily as applications interact with the database, thus avoiding long pause times.
Edit intent: fluency
Original:  We demonstrate performing updates to JSON values involving adding, deleting,and updating, and modifying JSON fields, and also demonstrate modifications to the key names .
Revised:  We demonstrate performing updates to the data stored in Redis from programs with backward-incompatible naming and format changes .
Edit intent: clarity
Original:  We find that our system has only around 4.95\%-8.6\% overhead in general use cases, and that the pause time during lazy updatesis less than transforming the database all at once .
Revised:  We find that our system has only around 4.95\%-8.6\% overhead in general use and minimal impact during updates, which is a significant improvement over the lengthy pause times incurred when transforming the entire database offline .
Edit intent: clarity
Original:  The problem we address in this paper is: How can we support the evolution of high-availability applications and their NoSQL data online, without excessive delays or interruptions, even in the presence of backward-incompatible data- format changes?
Revised:  The problem we address in this paper is: How can we support the evolution of high-availability applications and their NoSQL data online, without excessive delays or interruptions, even in the presence of backward-incompatible data format changes?
Edit intent: fluency
Original:  We find that KVolve has essentially no overhead in general use and minimal impact during updates, which is a significant improvement over the lengthy pause times incurred when transforming the entire database offline .
Revised:  We find that KVolve has essentially no overhead in general use and minimal pause times during updates .
Edit intent: clarity
Original:  A handfull of such algorithms is given.
Revised:  A number of such algorithms is given.
Edit intent: clarity
Original:  Applied to a hundred of random data tables, these comparisons are in favor of two methods based on non-usual ratio-type formulas for the splitting procedures, namely the Silhouette criterion and the Dunn's criterion.
Revised:  Applied to a hundred of random data tables, these comparisons are in favor of two methods based on unusual ratio-type formulas for the splitting procedures, namely the Silhouette criterion and the Dunn's criterion.
Edit intent: fluency
Original:  Applied to a hundred of random data tables, these comparisons are in favor of two methods based on non-usual ratio-type formulas for the splitting procedures, namely the Silhouette criterion and the Dunn's criterion.
Revised:  Applied to a hundred of random data tables, these comparisons are in favor of two methods based on non-usual ratio-type formulas for the splitting procedures, namely the Silhouette criterion and Dunn's criterion.
Edit intent: fluency
Original:  Second, we show that the sampling distribution of a SGD algorithm can be estimated online by incrementally minimizing the variance of the gradient.
Revised:  Second, we show that the sampling distribution of an SGD algorithm can be estimated online by incrementally minimizing the variance of the gradient.
Edit intent: fluency
Original:  We show that AW-SGD yields faster convergence in three different applications: (i) image classification with deep features, where the sampling of images depends on their labels, (ii) matrix factorization, where rows and columns are not sampled uniformly, and (iii) reinforcement learning, where the optimized and explore policies are estimated at the same time  .
Revised:  We show that AWSGD yields faster convergence in three different applications: (i) image classification with deep features, where the sampling of images depends on their labels, (ii) matrix factorization, where rows and columns are not sampled uniformly, and (iii) reinforcement learning, where the optimized and explore policies are estimated at the same time .
Edit intent: clarity
Original:  We show that AW-SGD yields faster convergence in three different applications: (i) image classification with deep features, where the sampling of images depends on their labels, (ii) matrix factorization, where rows and columns are not sampled uniformly, and (iii) reinforcement learning, where the optimized and explore policies are estimated at the same time  .
Revised:  We show that AW-SGD yields faster convergence in three different applications: (i) image classification with deep features, where the sampling of images depends on their labels, (ii) matrix factorization, where rows and columns are not sampled uniformly, and (iii) reinforcement learning, where the optimized and exploration policies are estimated at the same time .
Edit intent: fluency
Original:  One of the key concepts in 5G cellular systems is a small cell network, which settles the high mobile traffic demand and provides uniform user-experienced data rates.
Revised:  One of the key concepts in 5G cellular systems is the small cell network, which settles the high mobile traffic demand and provides uniform user-experienced data rates.
Edit intent: fluency
Original:  This study validates the feasibility of the 3D hybrid beamforming, mostly for link-level performances, through the implementation of a real-time testbed using a software-defined radio (SDR) platform and fabricated antenna array.
Revised:  This study validates the feasibility of the 3D hybrid beamforming, mostly for link-level performances, through the implementation of a realtime testbed using a software-defined radio (SDR) platform and fabricated antenna array.
Edit intent: fluency
Original: Ligand diffusion through a protein interior is a fundamental process governing biological signaling and enzymatic catalysis.
Revised: Ligand diffusion through proteins is a fundamental process governing biological signaling and enzymatic catalysis.
Edit intent: clarity
Original:  A complex topology of channels in proteins leads often to difficulties in modeling ligand escape pathways by classical molecular dynamics simulations.
Revised:  The complex topology of channels in proteins leads often to difficulties in modeling ligand escape pathways by classical molecular dynamics simulations.
Edit intent: fluency
Original:  A complex topology of channels in proteins leads often to difficulties in modeling ligand escape pathways by classical molecular dynamics simulations.
Revised:  A complex topology of protein tunnels results in difficulties with computing ligand escape pathways by classical molecular dynamics simulations.
Edit intent: clarity
Original:  They are tested on three protein channels with increasing complexity  : M2 muscarinic GPCR receptor, enzyme nitrile hydrataseand heme-protein cytochrome P450cam.
Revised:  The methods are tested on three protein channels with increasing complexity : M2 muscarinic GPCR receptor, enzyme nitrile hydrataseand heme-protein cytochrome P450cam.
Edit intent: clarity
Original:  They are tested on three protein channels with increasing complexity  : M2 muscarinic GPCR receptor, enzyme nitrile hydrataseand heme-protein cytochrome P450cam.
Revised:  They are tested on three proteins with increasing complexity : M2 muscarinic GPCR receptor, enzyme nitrile hydrataseand heme-protein cytochrome P450cam.
Edit intent: fluency
Original:  They are tested on three protein channels with increasing complexity  : M2 muscarinic GPCR receptor, enzyme nitrile hydrataseand heme-protein cytochrome P450cam.
Revised:  They are tested on three protein channels with increasing complexity : M2 muscarinic receptor, nitrile hydratase, and cytochrome P450cam.
Edit intent: clarity
Original:  The proposed algorithms are general and appropriate in all problems where an accelerated transport of an object through a network of channels is studied .
Revised:  The proposed approach is general and appropriate in all problems where an accelerated transport of an object through a network of channels is studied .
Edit intent: clarity
Original:  The proposed algorithms are general and appropriate in all problems where an accelerated transport of an object through a network of channels is studied .
Revised:  The proposed algorithms are general and appropriate for accelerated transport of an object through a network of channels is studied .
Edit intent: clarity
Original:  The proposed algorithms are general and appropriate in all problems where an accelerated transport of an object through a network of channels is studied .
Revised:  The proposed algorithms are general and appropriate in all problems where an accelerated transport of an object through a network of protein tunnels .
Edit intent: clarity
Original:  In this paper, we identify an easy-to-compute lower bound on the smallest Hilbert space dimension needed to generate an arbitrary two-party quantum correlation.
Revised:  In this paper, we identify an easy-to-compute lower bound on the smallest Hilbert space dimension needed to generate a given two-party quantum correlation.
Edit intent: clarity
Original:  To derive the lower bound, we combine a new geometric characterization for the set of quantum correlations (arXiv:1506.07297) with techniques that were recently used to lower bound the PSD-rank of a nonnegative matrix, an important notion to mathematical optimization and quantum communication theory (arXiv:1407.4308).
Edit intent: coherence
Original:  We show that our bound is tight on the correlations generated by optimal quantum strategies for the CHSH  and the Magic Square Game and also reprove that a family of PR-boxes  cannot be realized using quantum strategies .
Revised:  We show that our bound is tight on the correlations generated by optimal quantum strategies for the CHSH Game and the Magic Square Game and also reprove that a family of PR-boxes cannot be realized using quantum strategies .
Edit intent: fluency
Original:  In this paper, we describe ReCon, a cross-platform system that reveals PII leaks and gives users control over them without requiring any special privileges or custom OSes.
Revised:  In this paper, we present the design, implementation, and evaluation of ReCon: a cross-platform system that reveals PII leaks and gives users control over them without requiring any special privileges or custom OSes.
Edit intent: clarity
Original:  We discuss the design and implementation of the system and evaluate its methodology with measurements from controlled experiments and flows from 16 users (19 devices) as part of an IRB-approved user study  .
Revised:  We evaluate ReCon's effectiveness with measurements from controlled experiments and flows from 16 users (19 devices) as part of an IRB-approved user study .
Edit intent: clarity
Original:  The distribution function of \alpha a_n~mod~2\pi seems to be supported on an interval of length \sim 3 and has a curious shape.
Revised:  The distribution function of \alpha a_n~mod~2\pi seems to have a very curious shape.
Edit intent: clarity
Original:  Indeed, for the first 10^7 elements of Ulam's sequence, we have \left( 2.5714474995~ a_n\right) < 0 \qquad for all~a_n \notin \left\{2, 3, 47, 69\right\}.
Revised:  Indeed, for the first 10^7 elements of Ulam's sequence, \left( 2.5714474995~ a_n\right) < 0 \qquad for all~a_n \notin \left\{2, 3, 47, 69\right\}.
Edit intent: coherence
Original:  We hope that this very rigid structure will eventually provide a way of understanding properties of the Ulam sequence and believe that the arising phenomenon might be of interest in itself .
Revised:  We hope that this very rigid structure as well as the the underlying generating mechanism should be worthy of further study .
Edit intent: clarity
Original:  consecutive differences do not seem to be periodic and can be large, e.g. a_{18858 purpose of this short note is to report the following empirical discovery: there seems to exist a real \alpha \sim 2.571447499 \dots such that \left\{\alpha a_n: n\in N\right\} \quad mod~2\pi \quad \mbox{generates an absolutely continuous non-uniform measure} that seems to be supported on a subset of T.
Revised:  the purpose of this short note is to report the following empirical discovery: there seems to exist a real \alpha \sim 2.571447499 \dots such that \left\{\alpha a_n: n\in N\right\} \quad mod~2\pi \quad \mbox{generates an absolutely continuous non-uniform measure} that seems to be supported on a subset of T.
Edit intent: coherence
Original:  consecutive differences do not seem to be periodic and can be large, e.g. a_{18858 purpose of this short note is to report the following empirical discovery: there seems to exist a real \alpha \sim 2.571447499 \dots such that \left\{\alpha a_n: n\in N\right\} \quad mod~2\pi \quad \mbox{generates an absolutely continuous non-uniform measure} that seems to be supported on a subset of T.
Revised:  consecutive differences do not seem to be periodic and can be large, e.g. a_{18858 purpose of this short note is to report the following empirical discovery: there seems to exist a real \alpha \sim 2.571447499 \dots such that \left\{\alpha a_n: n\in N\right\} \quad mod~2\pi \quad \mbox{generates an absolutely continuous non-uniform measure} that seems to be supported on a subset of T.
Edit intent: fluency
Original:  consecutive differences do not seem to be periodic and can be large, e.g. a_{18858 purpose of this short note is to report the following empirical discovery: there seems to exist a real \alpha \sim 2.571447499 \dots such that \left\{\alpha a_n: n\in N\right\} \quad mod~2\pi \quad \mbox{generates an absolutely continuous non-uniform measure} that seems to be supported on a subset of T.
Revised:  consecutive differences do not seem to be periodic and can be large, e.g. a_{18858 purpose of this short note is to report the following empirical discovery: there seems to exist a real \alpha \sim 2.571447499 \dots such that \left\{\alpha a_n: n\in N\right\} \quad mod~2\pi \quad \mbox{generates an absolutely continuous non-uniform measure} supported on a subset of T.
Edit intent: fluency
Original:  The distribution function of \alpha a_n~mod~2\pi seems to have a very curious shape.
Edit intent: coherence
Original:  Indeed, it follows from a formula of Landau that for any prime p, any m \in N%DIFDELCMD < \left\{ %%% 1 \leq n \leq N: \cos{\left( (p^m)~ t_n\right) < 0}%DIFDELCMD < \right\} %%% \geq \frac{N{2} + }%DIFDELCMD < \left(%%% \frac{N{N}}%DIFDELCMD < \right)%%%  .
Revised:  Indeed, it follows from a formula of Landau that for any prime p, any m \in N%DIFDELCMD < \left\{ %%% 1 \leq n \leq N: \cos{\left( (p^m)~ t_n\right) < 0}%DIFDELCMD < \right\} %%% {2} + }%DIFDELCMD < \left(%%% \frac{N{N}}%DIFDELCMD < \right)%%% .
Edit intent: clarity
Original:  Indeed, it follows from a formula of Landau that for any prime p, any m \in N%DIFDELCMD < \left\{ %%% 1 \leq n \leq N: \cos{\left( (p^m)~ t_n\right) < 0}%DIFDELCMD < \right\} %%% \geq \frac{N{2} + }%DIFDELCMD < \left(%%% \frac{N{N}}%DIFDELCMD < \right)%%%  .
Revised:  Indeed, it follows from a formula of Landau that for any prime p, any m \in N%DIFDELCMD < \left\{ %%% 1 \leq n \leq N: \cos{\left( (p^m)~ t_n\right) < 0}%DIFDELCMD < \right\} %%% \geq \frac{N{2} + }%DIFDELCMD < \left(%%% {N}}%DIFDELCMD < \right)%%% .
Edit intent: fluency
Original:  We show that the hidden-variable resultant method based on the Cayley (Dixon or B\'{e is inherently and spectacularly numerically unstable by a factor that grows exponentially with the dimension.
Revised:  We show that the hidden variable resultant method based on the Cayley (Dixon or B\'{e is inherently and spectacularly numerically unstable by a factor that grows exponentially with the dimension.
Edit intent: fluency
Original:  We also show that the Sylvester resultant for solving bivariate polynomial systems can square the condition number of the problem.
Revised:  We also show that the Sylvester matrix for solving bivariate polynomial systems can square the condition number of the problem.
Edit intent: clarity
Original:  In other words, two popular hidden-variable resultant methods are numerically unstable, and this mathematically explains the difficulties that are frequently reported by practitioners  . Along the way, we prove that the Cayley resultant is a generalization of Cramer's rule for solving linear systems and generalize Clenshaw's algorithm to an evaluation scheme for polynomials expressed in a degree-graded polynomial basis.
Revised:  In other words, two popular hidden variable resultant methods are numerically unstable, and this mathematically explains the difficulties that are frequently reported by practitioners . Along the way, we prove that the Cayley resultant is a generalization of Cramer's rule for solving linear systems and generalize Clenshaw's algorithm to an evaluation scheme for polynomials expressed in a degree-graded polynomial basis.
Edit intent: fluency
Original:  By factorizing an original matrix to low-rank matrices, MF provides a unified method for dimesion reduction, clustering, and matrix completion.
Revised:  By factorizing an original matrix to low-rank matrices, MF provides a unified method for dimension reduction, clustering, and matrix completion.
Edit intent: fluency