wanyu/IteraTeR_v2 huggingface dataset:
Original:  In this paper, we use the Response Functions (RFs), that is the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues \lambda%DIFDELCMD < } %%% = 0, +/- i \omega%DIFDELCMD < } %%% to predict the filament tension of the alternative vortices.
Revised:  In this paper, we use the Response Functions (RFs), that is the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues %DIFDELCMD < } %%% = 0, +/- i \omega%DIFDELCMD < } %%% to predict the filament tension of the alternative vortices.
Edit intent: clarity
Original:  In this paper, we use the Response Functions (RFs), that is the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues \lambda%DIFDELCMD < } %%% = 0, +/- i \omega%DIFDELCMD < } %%% to predict the filament tension of the alternative vortices.
Revised:  In this paper, we use the Response Functions (RFs), that is the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues \lambda%DIFDELCMD < } %%% = 0, +/- i %DIFDELCMD < } %%% to predict the filament tension of the alternative vortices.
Edit intent: clarity
Original:  In this paper, we use the Response Functions (RFs), that is the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues \lambda%DIFDELCMD < } %%% = 0, +/- i \omega%DIFDELCMD < } %%% to predict the filament tension of the alternative vortices.
Revised:  In this paper, we use the Response Functions (RFs), that is the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues \lambda%DIFDELCMD < } %%% = 0, +/- i \omega%DIFDELCMD < } %%% Response Functions are used to predict the filament tension of the alternative vortices.
Edit intent: clarity
Original: The elliptic Monge-Amp\`ere equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, elasticity, geometric optics, image processing and image registration.
Revised: The elliptic Monge-Ampere equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, elasticity, geometric optics, image processing and image registration.
Edit intent: fluency
Original:  In this article we build a finite difference solver for the Monge-Amp\'ere equation, which converges even for singular solutions.
Revised:  In this article we build a finite difference solver for the Monge-Ampere equation, which converges even for singular solutions.
Edit intent: fluency
Original:  The factors are: the gradient of the cell-to-cell coupling strength, the macroscopic gradient of excitability /automaticity, and microscopic heterogeneity of individual cells.
Revised:  The factors are: the gradient of the cell-to-cell coupling and cell excitability and microscopic heterogeneity of individual cells.
Edit intent: clarity
Original:  Interplay between these factors explains why newly generated organizing centres of sub-millimiter scale re-entrant waves of excitation can be dragged with the ischaemia boundary, transiently pinned due to local inhomogeneities, followed by penetration into the bulk of the tissue reaching macroscopic scales.
Revised:  The interplay between these factors explains why newly generated organizing centres of sub-millimiter scale re-entrant waves of excitation can be dragged with the ischaemia boundary, transiently pinned due to local inhomogeneities, followed by penetration into the bulk of the tissue reaching macroscopic scales.
Edit intent: fluency
Original:  Interplay between these factors explains why newly generated organizing centres of sub-millimiter scale re-entrant waves of excitation can be dragged with the ischaemia boundary, transiently pinned due to local inhomogeneities, followed by penetration into the bulk of the tissue reaching macroscopic scales.
Revised:  Interplay between these factors allows one to explain how spirals form, drift together with the moving boundary, get transiently pinned to local inhomogeneities, followed by penetration into the bulk of the tissue reaching macroscopic scales.
Edit intent: clarity
Original:  Interplay between these factors explains why newly generated organizing centres of sub-millimiter scale re-entrant waves of excitation can be dragged with the ischaemia boundary, transiently pinned due to local inhomogeneities, followed by penetration into the bulk of the tissue reaching macroscopic scales.
Revised:  Interplay between these factors explains why newly generated organizing centres of sub-millimiter scale re-entrant waves of excitation can be dragged with the ischaemia boundary, transiently pinned due to local inhomogeneities, and finally penetrate into the bulk of the tissue reaching macroscopic scales.
Edit intent: coherence
Original:  First approach is noncommittal, making no assumptions about properties of uncertainty or parameters of stimulation , as in Gepshtein, Tyukin, and Albright (2010) .
Revised:  First approach is noncommittal, making no assumptions about properties of uncertainty or parameters of stimulation .
Edit intent: coherence
Original:  The two approaches follow similar logic, except in one case maximal *uncertainty* is minimized and in the other minimal *certainty* is maximized.
Revised:  The two approaches follow similar logic, except in one case maximal uncertainty is minimized, and in the other minimal *certainty* is maximized.
Edit intent: fluency
Original:  The two approaches follow similar logic, except in one case maximal *uncertainty* is minimized and in the other minimal *certainty* is maximized.
Revised:  The two approaches follow similar logic, except in one case maximal *uncertainty* is minimized and in the other minimal certainty is maximized.
Edit intent: fluency
Original:  Recently, Aaronson A09%DIFDELCMD < ] %DIFDELCMD < %%% proposed a natural problem based on the DFT, and a conjecture - the "GLN conjecture" - about the power of AC_0, that would imply the existence of an oracle relative to which BQP is not in PH.
Revised:  A09%DIFDELCMD < ] %DIFDELCMD < %%% proposed a natural problem based on the DFT, and a conjecture - the "GLN conjecture" - about the power of AC_0, that would imply the existence of an oracle relative to which BQP is not in PH.
Edit intent: coherence
Original:  Recently, Aaronson A09%DIFDELCMD < ] %DIFDELCMD < %%% proposed a natural problem based on the DFT, and a conjecture - the "GLN conjecture" - about the power of AC_0, that would imply the existence of an oracle relative to which BQP is not in PH.
Revised:  Recently, Aaronson %DIFDELCMD < ] %DIFDELCMD < %%% proposed a natural problem based on the DFT, and a conjecture - the "GLN conjecture" - about the power of AC_0, that would imply the existence of an oracle relative to which BQP is not in PH.
Edit intent: fluency
Original:  2. We show that our conjecture (by itself) implies the existence of an oracle relative to which BQP is not in the PH.
Revised:  2. We show that our conjecture implies the existence of an oracle relative to which BQP is not in the PH.
Edit intent: clarity
Original:  This entails giving an explicit construction of unitary matrices, realizable by small quantum circuits, whose row-supports are "nearly-disjoint." 3. We give a simple framework (generalizing the setting of  [ A09 ]) in which any efficiently quantumly computable unitary gives rise to a distribution that can be distinguished from the uniform distribution by an efficient quantum algorithm.
Revised:  This entails giving an explicit construction of unitary matrices, realizable by small quantum circuits, whose row-supports are "nearly-disjoint." (2) We give a simple framework (generalizing the setting of [ A09 ]) in which any efficiently quantumly computable unitary gives rise to a distribution that can be distinguished from the uniform distribution by an efficient quantum algorithm.
Edit intent: coherence
Original: Constraint satisfaction problems (or CSPs) have been extensively studied in AI, database theory, graph theory, etc.
Revised: Constraint satisfaction problems (or CSPs) have been extensively studied in , for instance, artificial intelligence, database theory, graph theory, etc.
Edit intent: coherence
Original:  namely, all such counting problems are neatly classified into three categories under polynomial-time approximation-preserving reductions Dyer, Goldberg, and Jerrum, 2010 . We extend this result to approximate counting for complex-weighted Boolean CSPs, provided that all arity-1 constraints are freely available to use .
Revised:  namely, all such counting problems are neatly classified into three categories under polynomial-time approximation-preserving reductions . We extend this result to approximate counting for complex-weighted Boolean CSPs, provided that all arity-1 constraints are freely available to use .
Edit intent: coherence
Original:  This makes a significant progress in the quest for the approximation classification of all counting Boolean CSPsin the most general form .
Revised:  This makes a significant progress in the quest for making an approximation classification of all counting Boolean CSPsin the most general form .
Edit intent: fluency
Original:  To deal with complex weights, we employ proof techniques along the line of solving Holant problems Valiant, 2002, 2008 . Our result also gives an approximation version of the dichotomy theorem of the complexity of exact counting for such complex-weighted Boolean CSPs Cai, Lu, and Xia, 2009 .
Revised:  To deal with complex weights, we employ proof techniques along the line of solving Holant problems . Our result also gives an approximation version of the dichotomy theorem of the complexity of exact counting for such complex-weighted Boolean CSPs Cai, Lu, and Xia, 2009 .
Edit intent: coherence
Original:  To deal with complex weights, we employ proof techniques along the line of solving Holant problems Valiant, 2002, 2008 . Our result also gives an approximation version of the dichotomy theorem of the complexity of exact counting for such complex-weighted Boolean CSPs Cai, Lu, and Xia, 2009 .
Revised:  To deal with complex weights, we employ proof techniques along the line of solving Holant problems Valiant, 2002, 2008 . Our result also gives an approximation analogue of the dichotomy theorem of the complexity of exact counting for such complex-weighted Boolean CSPs Cai, Lu, and Xia, 2009 .
Edit intent: clarity
Original:  To deal with complex weights, we employ proof techniques along the line of solving Holant problems Valiant, 2002, 2008 . Our result also gives an approximation version of the dichotomy theorem of the complexity of exact counting for such complex-weighted Boolean CSPs Cai, Lu, and Xia, 2009 .
Revised:  To deal with complex weights, we employ proof techniques along the line of solving Holant problems Valiant, 2002, 2008 . Our result also gives an approximation version of the dichotomy theorem on the complexity of exact counting for such complex-weighted Boolean CSPs Cai, Lu, and Xia, 2009 .
Edit intent: fluency
Original:  To deal with complex weights, we employ proof techniques along the line of solving Holant problems Valiant, 2002, 2008 . Our result also gives an approximation version of the dichotomy theorem of the complexity of exact counting for such complex-weighted Boolean CSPs Cai, Lu, and Xia, 2009 .
Revised:  To deal with complex weights, we employ proof techniques along the line of solving Holant problems Valiant, 2002, 2008 . Our result also gives an approximation version of the dichotomy theorem of the complexity of exact counting for complex-weighted Boolean CSPs Cai, Lu, and Xia, 2009 .
Edit intent: clarity
Original:  To deal with complex weights, we employ proof techniques along the line of solving Holant problems Valiant, 2002, 2008 . Our result also gives an approximation version of the dichotomy theorem of the complexity of exact counting for such complex-weighted Boolean CSPs Cai, Lu, and Xia, 2009 .
Revised:  To deal with complex weights, we employ proof techniques along the line of solving Holant problems Valiant, 2002, 2008 . Our result also gives an approximation version of the dichotomy theorem of the complexity of exact counting for such complex-weighted Boolean CSPs .
Edit intent: coherence
Original:  When one tries to count approximately the total number of truth assignments that satisfy all Boolean constraints for (unweighted) Boolean CSPs, there is a known trichotomy theorem;
Revised:  When one tries to approximate the total number of truth assignments that satisfy all Boolean constraints for (unweighted) Boolean CSPs, there is a known trichotomy theorem;
Edit intent: clarity
Original:  We extend this result to approximate counting for complex-weighted Boolean CSPs, provided that all complex-valued unary constraints are freely available  .
Revised:  We extend this result to approximate counting for complex-weighted Boolean CSPs, provided that all complex-valued unary constraints are freely available to use .
Edit intent: clarity
Original:  The expressive power of those unary constraints enables us to prove a strong and complete classification theorem.
Revised:  The expressive power of those unary constraints enables us to prove a stronger, complete classification theorem.
Edit intent: fluency
Original:  This makes a significant progress in the quest for making an approximation classification of all counting CSPs.
Revised:  This makes a step forward in the quest for making an approximation classification of all counting CSPs.
Edit intent: clarity
Original:  We introduce a novel notion of T-constructibility that naturally indices approximation-preserving reducibility.
Revised:  We introduce a novel notion of T-constructibility that naturally induces approximation-preserving reducibility.
Edit intent: fluency
Original:  From a practical viewpoint, it is beneficial to approximately solve  CSPs.
Revised:  From a practical viewpoint, it is beneficial to approximately solve those CSPs.
Edit intent: clarity
Original:  namely, all such counting problems are neatly classified into  three categories under polynomial-time  approximation-preserving reductions.
Revised:  namely, all such counting problems are neatly classified into exactly three categories under polynomial-time approximation-preserving reductions.
Edit intent: coherence
Original:  The expressive power of those unary constraints enables us to prove  a stronger, complete classification theorem.
Revised:  It is the expressive power of those unary constraints enables us to prove a stronger, complete classification theorem.
Edit intent: coherence
Original:  The expressive power of those unary constraints enables us to prove  a stronger, complete classification theorem.
Revised:  The expressive power of free unary constraints that enables us to prove a stronger, complete classification theorem.
Edit intent: clarity
Original:  The expressive power of those unary constraints enables us to prove  a stronger, complete classification theorem.
Revised:  The expressive power of those unary constraints enables us to prove such a stronger, complete classification theorem.
Edit intent: clarity
Original:  This  makes a step forward in the quest for the approximation-complexity classification of all counting CSPs.
Revised:  This discovery makes a step forward in the quest for the approximation-complexity classification of all counting CSPs.
Edit intent: clarity
Original:  We introduce a novel notion of T-constructibility that naturally induces approximation-preserving reducibility.
Revised:  Moreover, we introduce a novel notion of T-constructibility that naturally induces approximation-preserving reducibility.
Edit intent: coherence
Original:  We show here that subband partitioning also provides improved opportunities for short-range communication with minimal effect onto the macrocells .
Revised:  We show here that subband partitioning also provides improved opportunities for short-range communication as well .
Edit intent: clarity
Original:  Moreover, the proposed load-spillage power control scheme requires minimal interference coordination communication between the femtos and macros, which is often one of the main challenges in femtocell interference control .
Revised:  Moreover, the proposed scheme requires minimal interference coordination communication between the femtos and macros, which is often one of the main challenges in femtocell interference control .
Edit intent: clarity
Original:  Moreover, the proposed load-spillage power control scheme requires minimal interference coordination communication between the femtos and macros, which is often one of the main challenges in femtocell interference control .
Revised:  Moreover, the proposed load-spillage power control scheme requires minimal interference coordination communication between the femtos and macros, which is one of the main challenges in femtocell interference control .
Edit intent: coherence
Original:  Moreover, the proposed load-spillage power control scheme requires minimal interference coordination communication between the femtos and macros, which is often one of the main challenges in femtocell interference control .
Revised:  Moreover, the proposed load-spillage power control scheme requires minimal interference coordination communication between the femtos and macros, which is often one of the main challenges in femtocell systems .
Edit intent: clarity
Original:  Further modest gains are also possible with successive interference cancelation.
Revised:  Further modest gains may also be possible with interference cancelation.
Edit intent: clarity
Original:  We answer this question in terms of the long term success probability of transactions for various network topologies and credit values.
Revised:  We answer this question in terms of the long term failure probability of transactions for various network topologies and credit values.
Edit intent: fluency
Original:  A natural question to ask in this setting is: how long can the network sustain liquidity, i.e. \ how long can the network support the routing of payments before credit dries up?
Revised:  A natural question to ask in this setting is: how long can the network sustain liquidity, i.e. , how long can the network support the routing of payments before credit dries up?
Edit intent: fluency
Original:  We show that under symmetric transaction rates, the transaction failure probability in a number of well-known graph families goes to zero as the size, the density or the credit capacity of the network increases.
Revised:  We show that under symmetric transaction rates, the transaction failure probability in a number of well-known graph families goes to zero as the size, density or credit capacity of the network increases.
Edit intent: fluency
Original: Independent component analysis (ICA) is a computational method for separating a multivariate signal into subcomponents supposing the mutual statistical independence of the non-Gaussian source signals.
Revised: Independent component analysis (ICA) is a computational method for separating a multivariate signal into subcomponents assuming the mutual statistical independence of the non-Gaussian source signals.
Edit intent: fluency
Original:  The classical Independent Components Analysis (ICA) framework usually assumes linear combinations of independent sources over the field of real-valued numbers R.
Revised:  The classical Independent Components Analysis (ICA) framework usually assumes linear combinations of independent sources over the field of realvalued numbers R.
Edit intent: fluency
Original:  We also consider the inverse problem of inferring the values of latent variables  with noisy measurements.
Revised:  The inverse problem concerning inferring the values of latent variables with noisy measurements.
Edit intent: clarity
Original:  The effectiveness of the proposed algorithms is demonstrated through simulations .
Revised:  We conduct an extensive simulation study to verify the effectiveness of the proposed algorithms is demonstrated through simulations .
Edit intent: clarity
Original:  The effectiveness of the proposed algorithms is demonstrated through simulations .
Revised:  The effectiveness of the propose algorithm and present examples of real-world applications where bICA can be applied .
Edit intent: clarity
Original: Music Sight Reading is a complex process that when it is occurred in the brain , some learning attributes would be emerged.
Revised: Music Sight Reading is a complex process in which when it is occurred in the brain , some learning attributes would be emerged.
Edit intent: clarity
Original: Music Sight Reading is a complex process that when it is occurred in the brain , some learning attributes would be emerged.
Revised: Music Sight Reading is a complex process that when it is occurred in the brain some learning attributes would be emerged.
Edit intent: fluency
Original:  The model we offer here is a computational model on which an updated weights equation to fixing the weights is accompanied too.
Revised:  The model we offer here is a computational model on which an updated weights equation to fix the weights is accompanied too.
Edit intent: fluency
Original:  The first property is ID and the other  is maximal commutativity  .
Revised:  The first property is ID and the other property is maximal commutativity .
Edit intent: fluency
Original:  A semigroup has the ID property if the only infinite invariant  set (with respect to the semigroup 's action) is the entire space.
Revised:  A semigroup has the ID property if the only infinite invariant set (with respect to the semigroup action) is the entire space.
Edit intent: clarity
Original:  One semigroup is spanned by cellular automata  that represent multiplications in R/Z and the other semigroup consists of all the linear cellular automata (when taking the symbol set to be Z/nZ . It will be shown that these two semigroups are having the ID property and that they both maximal commutative.
Revised:  One semigroup is spanned by cellular automata that represent multiplications in R/Z and the other one consists of all the linear cellular automata (when taking the symbol set to be Z/nZ . It will be shown that these two semigroups are having the ID property and that they both maximal commutative.
Edit intent: clarity
Original:  We consider the relationship, with respect to these properties, between semigroups which act on the one sided shift space and semigroups acting on the two sided shift space .
Revised:  We consider the relationship, with respect to these properties, between semigroups which act on the one sided shift space a semigroup acting on a two sided shift space .
Edit intent: clarity
Original:  By adding some regularity conditions, the latter functions coincide with the Lov\'asz extensions vanishing at the origin, which subsume the discrete Choquet integrals.
Revised:  By adding some regularity conditions, these functions coincide with the Lov\'asz extensions vanishing at the origin, which subsume the discrete Choquet integrals.
Edit intent: clarity
Original:  Memory is designed below to learn such sequences , that is, to detect their existence and if prompted, to run them without central processing involvement.
Revised:  Memory is designed below to detect those sequences of actions that have been repeated a given number n. Subsequently such sequences are permitted to run without CPU involvement. This mimics human learning. Actions are rehearsed and once learned, they are performed automatically without conscious involvement.
Edit intent: clarity
Original:  The second is based on parameter estimates found in SARS literature.
Revised:  The second is based on parameter estimates found in the literature.
Edit intent: clarity
Original:  We will seethat these two definitions coincide.
Revised:  As we will see, these two definitions coincide.
Edit intent: fluency
Original:  We prove that the languages recognized by linear recurrence equations with coefficients in P(\Sigma) are precisely the regular languages.
Edit intent: coherence