wanyu/IteraTeR_v2 huggingface dataset:
Original:  with%DIFDELCMD < align* %DIFDELCMD < tk<\frac{t-1{t}} align* %%% for certain fixed\leq\epsilon, provided that the tk-order restricted isometry constant (RIC) of A satisfies a certain constraint related to } t> 1. Recently, this condition for t%DIFDELCMD < \geq4%%%  /3 has been proved by Cai and Zhang (2014) to be sharp for exactly recovering any rank-k matrices via the constrained Nuclear Norm Minimization (NNM).
Revised:  with%DIFDELCMD < align* %DIFDELCMD < tk<\frac{t-1{t}} align* %%% for certain fixed\leq\epsilon, provided that the tk-order restricted isometry constant (RIC) of A satisfies a certain constraint related to } t> 1. Recently, this condition for t%DIFDELCMD < \geq4%%% /3 has been proved by Cai and Zhang (2014) to be sharp for exactly recovering any rank-k matrix via the constrained Nuclear Norm Minimization (NNM).
Edit intent: fluency
Original:  For simplifying the task of defining correct monad transformers, we propose a language inspired by Moggi's monadic metalanguage that is parameterized by a dependent type theory.
Revised:  For defining correct monad transformers, we propose a language inspired by Moggi's monadic metalanguage that is parameterized by a dependent type theory.
Edit intent: clarity
Original:  We implement our framework in both Coq and F*, and illustrate that it supports a wide variety of verification styles for effects such as partiality, exceptions, nondeterminism, state, and input-output  .
Revised:  We implement our framework in both Coq and F*, and illustrate that it supports a wide variety of verification styles for effects such as exceptions, nondeterminism, state, and input-output .
Edit intent: clarity
Original:  We implement our framework in both Coq and F*, and illustrate that it supports a wide variety of verification styles for effects such as partiality, exceptions, nondeterminism, state, and input-output  .
Revised:  We implement our framework in both Coq and F*, and illustrate that it supports a wide variety of verification styles for effects such as partiality, exceptions, nondeterminism, state, input-output .
Edit intent: fluency
Original:  In this paper, we first prove that a polynomial interpolant of the form h( %DIFDELCMD < \xx%%%  )>0 exists for two mutually contradictory polynomial formulas \phi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy%%%  ) and \psi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%%  ), with the form f_1\ge0\wedge\cdots\wedge f_n\ge0, where f_i are polynomials in %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy %%% or%DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%%  , and the quadratic module generated by f_i is Archimedean.
Revised:  In this paper, we first prove that a polynomial interpolant of the form h( %DIFDELCMD < \xx%%% )>0 exists for two mutually contradictory polynomial formulas \phi( %DIFDELCMD < \xx%%% %DIFDELCMD < \yy%%% ) and \psi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%% ), with the form f_1\ge0\wedge\cdots\wedge f_n\ge0, where f_i are polynomials in %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy %%% or%DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%% , and the quadratic module generated by f_i is Archimedean.
Edit intent: fluency
Original:  In this paper, we first prove that a polynomial interpolant of the form h( %DIFDELCMD < \xx%%%  )>0 exists for two mutually contradictory polynomial formulas \phi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy%%%  ) and \psi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%%  ), with the form f_1\ge0\wedge\cdots\wedge f_n\ge0, where f_i are polynomials in %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy %%% or%DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%%  , and the quadratic module generated by f_i is Archimedean.
Revised:  In this paper, we first prove that a polynomial interpolant of the form h( %DIFDELCMD < \xx%%% )>0 exists for two mutually contradictory polynomial formulas \phi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy%%% ) and \psi( %DIFDELCMD < \xx%%% %DIFDELCMD < \zz%%% ), with the form f_1\ge0\wedge\cdots\wedge f_n\ge0, where f_i are polynomials in %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy %%% or%DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%% , and the quadratic module generated by f_i is Archimedean.
Edit intent: fluency
Original:  In this paper, we first prove that a polynomial interpolant of the form h( %DIFDELCMD < \xx%%%  )>0 exists for two mutually contradictory polynomial formulas \phi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy%%%  ) and \psi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%%  ), with the form f_1\ge0\wedge\cdots\wedge f_n\ge0, where f_i are polynomials in %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy %%% or%DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%%  , and the quadratic module generated by f_i is Archimedean.
Revised:  In this paper, we first prove that a polynomial interpolant of the form h( %DIFDELCMD < \xx%%% )>0 exists for two mutually contradictory polynomial formulas \phi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy%%% ) and \psi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%% ), with the form f_1\ge0\wedge\cdots\wedge f_n\ge0, where f_i are polynomials in %DIFDELCMD < \xx%%% %DIFDELCMD < \yy %%% or%DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%% , and the quadratic module generated by f_i is Archimedean.
Edit intent: fluency
Original:  In this paper, we first prove that a polynomial interpolant of the form h( %DIFDELCMD < \xx%%%  )>0 exists for two mutually contradictory polynomial formulas \phi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy%%%  ) and \psi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%%  ), with the form f_1\ge0\wedge\cdots\wedge f_n\ge0, where f_i are polynomials in %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy %%% or%DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%%  , and the quadratic module generated by f_i is Archimedean.
Revised:  In this paper, we first prove that a polynomial interpolant of the form h( %DIFDELCMD < \xx%%% )>0 exists for two mutually contradictory polynomial formulas \phi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy%%% ) and \psi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%% ), with the form f_1\ge0\wedge\cdots\wedge f_n\ge0, where f_i are polynomials in %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy %%% %DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%% , and the quadratic module generated by f_i is Archimedean.
Edit intent: coherence
Original:  In this paper, we first prove that a polynomial interpolant of the form h( %DIFDELCMD < \xx%%%  )>0 exists for two mutually contradictory polynomial formulas \phi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy%%%  ) and \psi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%%  ), with the form f_1\ge0\wedge\cdots\wedge f_n\ge0, where f_i are polynomials in %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy %%% or%DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%%  , and the quadratic module generated by f_i is Archimedean.
Revised:  In this paper, we first prove that a polynomial interpolant of the form h( %DIFDELCMD < \xx%%% )>0 exists for two mutually contradictory polynomial formulas \phi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy%%% ) and \psi( %DIFDELCMD < \xx%%% ,%DIFDELCMD < \zz%%% ), with the form f_1\ge0\wedge\cdots\wedge f_n\ge0, where f_i are polynomials in %DIFDELCMD < \xx%%% ,%DIFDELCMD < \yy %%% or%DIFDELCMD < \xx%%% %DIFDELCMD < \zz%%% , and the quadratic module generated by f_i is Archimedean.
Edit intent: fluency
Original:  We introduce a nonlinear stochastic model accounting for the joint dynamics of  two cell types, either precursor or proliferative cells.
Revised:  We introduce a nonlinear stochastic model accounting for the joint dynamics of the two cell types, either precursor or proliferative cells.
Edit intent: fluency
Original:  Using the probabilistic theory of first passage times, we design a numerical scheme based on a rigorous Finite State Projection and coupling techniques to assess the mean extinction time and the cell number at extinction time.
Revised:  Using the probabilistic theory of first passage times, we design a numerical scheme based on a rigorous Finite State Projection and coupling techniques to compute the mean extinction time and the cell number at extinction time.
Edit intent: clarity
Original:  We also obtain analytical formulas for an approximating branching process .
Revised:  We find that the feedback term clearly lowers the number of proliferative cells at the extinction time .
Edit intent: coherence
Original:  We calibrate the model parameters using an exact likelihood approach using both experimental and in-silico datasets .
Revised:  We calibrate the model parameters using an exact likelihood approach .
Edit intent: clarity
Original:  We carry out a comprehensive comparison between the initial model and a series of submodels, which help to select the critical cell events taking place during activation .
Revised:  We carry out a comprehensive comparison between the initial model and a series of submodels, which helps to select the critical cell events taking place during activation .
Edit intent: fluency
Original: Funding the production and distribution of quality online content is an open problem for content producers.
Revised: Funding the production of quality online content is an open problem for content producers.
Edit intent: clarity
Original: Funding the production and distribution of quality online content is an open problem for content producers.
Revised: Funding the production and distribution of quality online content is a pressing problem for content producers.
Edit intent: clarity
Original:  Decreasing revenues from digital advertising, along with increasing ad fraud, have driven publishers to " lock " their content behind paywalls, thus denying access to non-subscribed users .
Revised:  Decreasing revenues from digital advertising, along with increasing ad fraud, have driven publishers to " pay-for-access " their content behind paywalls, thus denying access to non-subscribed users .
Edit intent: clarity
Original: This paper presents a two-level protein folding optimization on a three-dimensional AB off-lattice model.
Revised: This paper presents a two-phase protein folding optimization on a three-dimensional AB off-lattice model.
Edit intent: clarity
Original:  The first level is responsible for forming conformations with a good hydrophobic core or a set of compact hydrophobic amino acid positions.
Revised:  The first phase is responsible for forming conformations with a good hydrophobic core or a set of compact hydrophobic amino acid positions.
Edit intent: clarity
Original:  These conformations are forwarded to the second level , where an accurate search is performed with the aim of locating conformations with the best energy value.
Revised:  These conformations are forwarded to the second phase , where an accurate search is performed with the aim of locating conformations with the best energy value.
Edit intent: clarity
Original:  The optimization process switches between these two levels until the stopping condition is satisfied.
Revised:  The optimization process switches between these two phases until the stopping condition is satisfied.
Edit intent: clarity
Original:  An auxiliary fitness function was designed for the first level , while the original fitness function is used in the second level .
Revised:  An auxiliary fitness function was designed for the first phase , while the original fitness function is used in the second level .
Edit intent: clarity
Original:  An auxiliary fitness function was designed for the first level , while the original fitness function is used in the second level .
Revised:  An auxiliary fitness function was designed for the first level , while the original fitness function is used in the second phase .
Edit intent: clarity
Original:  The auxiliary fitness function includes  expression about the quality of the hydrophobic core.
Revised:  The auxiliary fitness function includes an expression about the quality of the hydrophobic core.
Edit intent: fluency
Original:  Our differential evolution algorithm was used for demonstrating the efficiency of the two-level optimization.
Revised:  Our differential evolution algorithm was used for demonstrating the efficiency of two-phase optimization.
Edit intent: clarity
Original:  The obtained experimental results show that the employed two-level optimization improves the efficiency of our algorithm significantly , and that the proposed algorithm is superior to other state-of-the-art algorithms.
Revised:  The obtained experimental results show that the employed two-phase optimization improves the efficiency of our algorithm significantly , and that the proposed algorithm is superior to other state-of-the-art algorithms.
Edit intent: clarity
Original:  The obtained experimental results show that the employed two-level optimization improves the efficiency of our algorithm significantly , and that the proposed algorithm is superior to other state-of-the-art algorithms.
Revised:  The obtained experimental results show that the employed two-level optimization improves the efficiency of our algorithm significantly and that the proposed algorithm is superior to other state-of-the-art algorithms.
Edit intent: fluency
Original:  Inspired by humans' natural neurobiological filtering process, a central component of our policy network design is an information gating function, termed the Kinesic-Proxemic-Message Gate (KPM-Gate) , that models the ability of an agent to selectively gather information from specific neighboring agents.
Revised:  Inspired by humans' natural neurobiological filtering process, a central component of MGpi is the Kinesic-Proxemic-Message Gate (KPM-Gate) , that models the ability of an agent to selectively gather information from specific neighboring agents.
Edit intent: clarity
Original:  The degree of influence of a neighbor is based on dynamic non-verbal cues such as body motion, head pose (  kinesics) and interpersonal space (proxemics).
Revised:  The degree of influence of a neighbor is based on dynamic non-verbal cues such as body motion, head pose ( kinesics) and spatial behavior (proxemics).
Edit intent: clarity
Original:  We further show that Recognition is \mathsf{NP B_k-CPG  with k \geq -complete.
Revised:  The main result of the paper is that recognizing CPG graphs and B_k-CPG with k \geq -complete.
Edit intent: clarity
Original:  Moreover, we show that the same remains true even within the class of planar graphs in the case k \geq } 3. Additionally, we examine the computational complexity of several graph problems restricted to CPG graphs .
Revised:  Moreover, we show that the same remains true even within the class of planar graphs in the case k \geq } 3. We then consider several graph problems restricted to CPG graphs .
Edit intent: clarity
Original:  Our method not only allows using two different extrapolation points to evaluate gradients and adding the inertial force, but also takes advantage of randomly picking the block of variables to update.
Revised:  Our methods not only allow using two different extrapolation points to evaluate gradients and adding the inertial force, but also takes advantage of randomly picking the block of variables to update.
Edit intent: fluency
Original:  Our method not only allows using two different extrapolation points to evaluate gradients and adding the inertial force, but also takes advantage of randomly picking the block of variables to update.
Revised:  Our method not only allows using two different extrapolation points to evaluate gradients and adding the inertial force, but also take advantage of randomly picking the block of variables to update.
Edit intent: fluency
Original:  Moreover, our method does not require a restarting step, and as such, it is not a monotonically decreasing method.
Revised:  Moreover, our methods do not require a restarting step, and as such, it is not a monotonically decreasing method.
Edit intent: fluency
Original:  We deploy the proposed methods to solve non-negative matrix factorization (NMF) problems and show that they compete favourably with the state-of-the-art NMF algorithms.
Revised:  We deploy the proposed methods to solve non-negative matrix factorization (NMF) and show that they compete favourably with the state-of-the-art NMF algorithms.
Edit intent: clarity
Original: In this paper, we propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems.
Revised: We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems.
Edit intent: clarity
Original:  Our methods not only allow using two different extrapolation points to evaluate gradients and adding the inertial force , but also take advantage of randomly picking the block of variables to update .
Revised:  Our methods not only allow using two different extrapolation points to evaluate the gradients and to add the inertial force , but also take advantage of randomly picking the block of variables to update .
Edit intent: fluency
Original:  To prove the convergence of the whole generated sequence to a critical point, we modify the convergence proof recipe of Bolte, Sabach and Teboulle (Proximal alternating linearized minimization for non-convex and non-smooth problems, Math.
Revised:  To prove the convergence of the whole generated sequence to a critical point, we modify the convergence proof recipe of Bolte, Sabach and Teboulle (Proximal alternating linearized minimization for non-convex and 
Edit intent: clarity
Original:  We deploy the proposed methods to solve non-negative matrix factorization (NMF) and show that they compete favourably with the state-of-the-art NMF algorithms  .
Revised:  We deploy the proposed methods to solve non-negative matrix factorization (NMF) and show that they compete favorably with the state-of-the-art NMF algorithms .
Edit intent: fluency
Original:  We uncover the existence of an hidden structure in these matrix sequences, namely, we show that these are indeed an example of Generalized Locally Toeplitz (GLT) sequences.
Revised:  We uncover the existence of a hidden structure in these matrix sequences, namely, we show that these are indeed an example of Generalized Locally Toeplitz (GLT) sequences.
Edit intent: fluency
Original:  Finally  we exploit it to propose an optimal preconditioner strategy for the GMRES, and Flexible--GMRES methods.
Revised:  Finally , we exploit it to propose an optimal preconditioner strategy for the GMRES, and Flexible--GMRES methods.
Edit intent: fluency
Original:  Finally  we exploit it to propose an optimal preconditioner strategy for the GMRES, and Flexible--GMRES methods.
Revised:  Finally we exploit it to propose an optimal preconditioner strategy for the GMRES, and Flexible-GMRES methods.
Edit intent: fluency
Original:  Our experiments show that ReLZ is orders of magnitude faster than other alternatives to compute the (exact or approximate) LZ parsing, at the reasonable price of an approximation factor below 2.0 in practice , and sometimes below 1.05, to the size of LZ.
Revised:  Our experiments show that ReLZ is faster than existing alternatives to compute the (exact or approximate) LZ parsing, at the reasonable price of an approximation factor below 2.0 in practice , and sometimes below 1.05, to the size of LZ.
Edit intent: clarity
Original:  Our experiments show that ReLZ is orders of magnitude faster than other alternatives to compute the (exact or approximate) LZ parsing, at the reasonable price of an approximation factor below 2.0 in practice , and sometimes below 1.05, to the size of LZ.
Revised:  Our experiments show that ReLZ is orders of magnitude faster than other alternatives to compute the (exact or approximate) LZ parsing, at the reasonable price of an approximation factor below 2.0 in all tested scenarios , and sometimes below 1.05, to the size of LZ.
Edit intent: clarity
Original: Third-party modules play a critical role in IoT applications, which generate and analyze highly privacy-sensitive data.
Revised: Third-party code plays a critical role in IoT applications, which generate and analyze highly privacy-sensitive data.
Edit intent: clarity
Original:  Unlike traditional desktop and server settings, IoT devices are mostly single-purpose running a dedicated, single application.
Revised:  Unlike traditional desktop and server settings, IoT devices mostly run a dedicated, single application.
Edit intent: clarity
Original:  Yet the only practical data protection mechanisms available today for IoT developers are ad-hoc tools that are not designed to prevent data leaks from malicious or vulnerable third-party code imported into an application.
Edit intent: coherence
Original:  We present Pyronia, a privilege separation system for IoT applications written in high-level languages.
Revised:  We present Pyronia, a fine-grained access control system for IoT applications written in high-level languages.
Edit intent: clarity
Original:  Pyronia exploits developers' coarse-grained expectations about how imported third-party code operates to restrict access to files and devices, specific network destinations, and even in-memory data objects, at the level of individual library functions.
Revised:  Pyronia exploits developers' coarse-grained expectations about how imported third-party code operates to restrict access to files , devices, and specific network destinations, and even in-memory data objects, at the level of individual library functions.
Edit intent: fluency
Original:  Pyronia exploits developers' coarse-grained expectations about how imported third-party code operates to restrict access to files and devices, specific network destinations, and even in-memory data objects, at the level of individual library functions.
Revised:  Pyronia exploits developers' coarse-grained expectations about how imported third-party code operates to restrict access to files and devices, specific network destinations, at the granularity of individual functions.
Edit intent: clarity
Original:  To efficiently protect data as it flows through the application , Pyronia combines three access control techniques: system call interposition, call stack inspection, and memory protection domains.
Revised:  To efficiently protect such sensitive OS resources , Pyronia combines three access control techniques: system call interposition, call stack inspection, and memory protection domains.
Edit intent: clarity
Original:  To efficiently protect data as it flows through the application , Pyronia combines three access control techniques: system call interposition, call stack inspection, and memory protection domains.
Revised:  To efficiently protect data as it flows through the application , Pyronia combines three techniques: system call interposition, call stack inspection, and memory protection domains.
Edit intent: clarity
Original:  To efficiently protect data as it flows through the application , Pyronia combines three access control techniques: system call interposition, call stack inspection, and memory protection domains.
Revised:  To efficiently protect data as it flows through the application , Pyronia combines three access control techniques: system call interposition, stack inspection, and memory protection domains.
Edit intent: clarity
Original:  To efficiently protect data as it flows through the application , Pyronia combines three access control techniques: system call interposition, call stack inspection, and memory protection domains.
Revised:  To efficiently protect data as it flows through the application , Pyronia combines three access control techniques: system call interposition, call stack inspection, and memory domains.
Edit intent: fluency
Original:  This design obviates the need for prior unintuitive or error-prone data flow analysis or application re-architecting , while enforcing the developer's access policy at run time.
Revised:  This design avoids the need for prior unintuitive or error-prone data flow analysis or application re-architecting , while enforcing the developer's access policy at run time.
Edit intent: fluency
Original:  This design obviates the need for prior unintuitive or error-prone data flow analysis or application re-architecting , while enforcing the developer's access policy at run time.
Revised:  This design obviates the need for application refactoring, or unintuitive data flow analysis or application re-architecting , while enforcing the developer's access policy at run time.
Edit intent: clarity