wanyu/IteraTeR_v2 huggingface dataset:
Original:  In this note, we show that for any \alpha>1-%DIFDELCMD < \lfloor %%% t/2%DIFDELCMD < \rfloor %%% ^{-1 the generating function for (list) graph homomorphisms from G to H can be calculated in subexponential time \mathcal{O}%DIFDELCMD < \left(%%% 2^{ \left(}\right)}  | V(G) | ^{\alpha}%DIFDELCMD < \MBLOCKRIGHTBRACE\right) %%% in the class of P_t-free graphs G. As a corollary, we show that the number of 3-colourings of a P_t-free graph G can be found in subexponential time.
Revised:  In this note, we show that for any \alpha>1-%DIFDELCMD < \lfloor %%% t/2%DIFDELCMD < \rfloor %%% ^{-1 the generating function for (list) graph homomorphisms from G to H can be calculated in subexponential time \mathcal{O}%DIFDELCMD < \left(%%% 2^{ \left(}\right)} | V(G) | ^{\alpha}%DIFDELCMD < \MBLOCKRIGHTBRACE\right) %%% in the class of P_t-free graphs G. As a corollary, we show that the number of 3-colourings of a P_t-free graph G can be found in subexponential time.
Edit intent: fluency
Original:  On the other hand, no subexponential time algorithm exists for 4-colouribility of P_t-free graphs assuming the Exponential Time Hypothesis  .
Revised:  On the other hand, no subexponential time algorithm exists for 4-colourability of P_t-free graphs assuming the Exponential Time Hypothesis .
Edit intent: fluency
Original:  The design technique takes a method performing a series of subspace-searches and constructs a family of methods that share the same worst-case guarantees as the original method, and  includes a fixed-step first-order method.
Revised:  The design technique takes a method performing a series of subspace-searches and constructs a family of methods that share the same worst-case guarantees as the original method, and b) the family includes a fixed-step first-order method.
Edit intent: coherence
Original:  We show that this technique yields optimal methods in the smooth and non-smooth cases and derive new methods for these cases, including methods that forego knowledge of the problem parameters , at the cost of a one-dimensional line search per iteration  .
Revised:  We demonstrate the effectiveness of the approach by deriving optimal methods for the smooth and non-smooth cases and derive new methods for these cases, including methods that forego knowledge of the problem parameters , at the cost of a one-dimensional line search per iteration .
Edit intent: clarity
Original:  We show that this technique yields optimal methods in the smooth and non-smooth cases and derive new methods for these cases, including methods that forego knowledge of the problem parameters , at the cost of a one-dimensional line search per iteration  .
Revised:  We show that this technique yields optimal methods in the smooth and non-smooth cases , including new methods that forego knowledge of the problem parameters , at the cost of a one-dimensional line search per iteration .
Edit intent: coherence
Original:  We show that this technique yields optimal methods in the smooth and non-smooth cases and derive new methods for these cases, including methods that forego knowledge of the problem parameters , at the cost of a one-dimensional line search per iteration  .
Revised:  We show that this technique yields optimal methods in the smooth and non-smooth cases and derive new methods for these cases, including methods that forego knowledge of the problem parameters at the cost of a one-dimensional line search per iteration .
Edit intent: fluency
Original:  In the strongly convex case, we show how numerical tools can be used to perform the construction, and show that  resulting method offers an improved convergence rate compared to Nesterov's celebrated fast gradient method.
Revised:  In the strongly convex case, we show how numerical tools can be used to perform the construction, and show that the resulting method offers an improved convergence rate compared to Nesterov's celebrated fast gradient method.
Edit intent: fluency
Original:  To this end, we propose an interactive HUman and Machine cOoperation framework for ER, denoted by i-HUMO. Similar to the existing HUMO framework, i-HUMO enforces both precision and recall levels by dividing an ER workload between the human and the machine.
Revised:  To this end, we propose an interactive HUman and Machine cOoperation framework for ER, denoted by r-HUMO. Built on the existing HUMO framework, i-HUMO enforces both precision and recall levels by dividing an ER workload between the human and the machine.
Edit intent: clarity
Original:  To this end, we propose an interactive HUman and Machine cOoperation framework for ER, denoted by i-HUMO. Similar to the existing HUMO framework, i-HUMO enforces both precision and recall levels by dividing an ER workload between the human and the machine.
Revised:  To this end, we propose an interactive HUman and Machine cOoperation framework for ER, denoted by i-HUMO. Similar to the existing HUMO framework, i-HUMO enforces both precision and recall levels by partitioning an ER workload between the human and the machine.
Edit intent: fluency
Original:  However, i-HUMO is a major improvement over HUMO in that it is interactive: its process of human workload selection is optimized based on real-time risk analysis on human-labeled results as well as pre-specified machine metrics.
Revised:  However, i-HUMO is a major improvement over HUMO in that it is interactive: its process of human workload selection is optimized based on real-time risk analysis on human-labeled results as well as prespecified machine metrics.
Edit intent: fluency
Original:  Our construction adapts to any bank of filters chosen to represent the set of receptive profiles of simple cells , since it does not require any structure on the parameterization on the family.
Revised:  Our construction adapts to any bank of filters chosen to represent a set of receptive profiles of simple cells , since it does not require any structure on the parameterization on the family.
Edit intent: fluency
Original:  Our construction adapts to any bank of filters chosen to represent the set of receptive profiles of simple cells , since it does not require any structure on the parameterization on the family.
Revised:  Our construction adapts to any bank of filters chosen to represent the set of receptive profiles , since it does not require any structure on the parameterization on the family.
Edit intent: clarity
Original:  Our construction adapts to any bank of filters chosen to represent the set of receptive profiles of simple cells , since it does not require any structure on the parameterization on the family.
Revised:  Our construction adapts to any bank of filters chosen to represent the set of receptive profiles of simple cells , since it does not require any structure on the parameterization of the family.
Edit intent: fluency
Original:  We present encapsulator, a system for producing a time capsulethat preserves this context and provides end users with a self-contained environment.
Revised:  We present encapsulator, a self-contained environment.
Edit intent: clarity
Original:  Our solution is close to the vision of an executable paper in that it provides end users with a fully featured desktop environment for validating findings or conducting new researchthat builds on prior work .
Revised:  Our solution is close to the vision of an executable paper in that it provides end users with a fully featured desktop environment for reproducible research .
Edit intent: clarity
Original:  While these devices are usually computationally more powerful than their digital counterparts, they suffer from analog noise which does not allow to error control.
Revised:  While these devices are usually computationally more powerful than their digital counterparts, they suffer from analog noise which does not allow for error control.
Edit intent: fluency
Original:   We study the performance of these analog computers by simulating integro-differential models of fluid dynamicstype , nonlinear Volterra equations for population growth, and quantum models describing non-Markovian memory effects, among others.
Revised:  We study the performance of these analog computers by simulating integro-differential models related to fluid dynamics , nonlinear Volterra equations for population growth, and quantum models describing non-Markovian memory effects, among others.
Edit intent: clarity
Original: We consider the problem of bipartite community detection in networks, or more generally the network biclustering problem.
Revised: We study bipartite community detection in networks, or more generally the network biclustering problem.
Edit intent: clarity
Original:  To obtain the general consistency result, as part of the provable version of the algorithm, we introduce a sub-block partitioning scheme that is also computationally attractive, allowing for distributed implementation of the algorithm without sacrificing optimality.
Revised:  To obtain the consistency result, as part of the provable version of the algorithm, we introduce a sub-block partitioning scheme that is also computationally attractive, allowing for distributed implementation of the algorithm without sacrificing optimality.
Edit intent: coherence
Original:  The provable version of the algorithm is derived from a general blueprint for pseudo-likelihood biclustering algorithms that employ simple EM type updates.
Revised:  The provable algorithm is derived from a general blueprint for pseudo-likelihood biclustering algorithms that employ simple EM type updates.
Edit intent: clarity
Original:  The provable version of the algorithm is derived from a general blueprint for pseudo-likelihood biclustering algorithms that employ simple EM type updates.
Revised:  The provable version of the algorithm is derived from a general class of pseudo-likelihood biclustering algorithms that employ simple EM type updates.
Edit intent: clarity
Original:  Motivated by this, this paper conducts an experimental comparison for the effects of missing, inconsistent and conflicting data on classification , clustering, and regression algorithms.
Revised:  Motivated by this, this paper conducts an experimental comparison for the effects of missing, inconsistent and conflicting data on classification and clustering algorithms.
Edit intent: clarity
Original:  Compared to clipping-based methods , VoroCrust cells are full Voronoi cells, with convexity and fatness guarantees.
Revised:  Compared to state-of-the-art methods based on clipping , VoroCrust cells are full Voronoi cells, with convexity and fatness guarantees.
Edit intent: clarity
Original:  in particular, the capacity of the noiseless channel with (d, k) -constrained constant-weight inputs is characterized.
Revised:  in particular, the exponential growth-rate of the number of (d, k) -constrained constant-weight inputs is characterized.
Edit intent: clarity
Original:  in particular, the capacity of the noiseless channel with (d, k) -constrained constant-weight inputs is characterized.
Revised:  in particular, the capacity of the noiseless channel with (d, k) -constrained constant-weight sequences is characterized.
Edit intent: clarity
Original:  The results are relevant for magnetic and optical  storage systems, reader-to-tag RFID channels, and other communication models where bit-shift errors are dominant and where (d, k) -constrained sequences are used for modulation.
Revised:  The results are relevant for magnetic and optical information storage systems, reader-to-tag RFID channels, and other communication models where bit-shift errors are dominant and where (d, k) -constrained sequences are used for modulation.
Edit intent: clarity
Original:  Surprisingly, for simple and widely used objects such as rectangles, the problem is NP-hard even when all the rectangles are "anchored" at a  line with slope -1.
Revised:  Even for simple and widely used objects such as rectangles, the problem is NP-hard even when all the rectangles are "anchored" at a line with slope -1.
Edit intent: coherence
Original:  Surprisingly, for simple and widely used objects such as rectangles, the problem is NP-hard even when all the rectangles are "anchored" at a  line with slope -1.
Revised:  Surprisingly, for simple and widely-used geometric objects such as rectangles, the problem is NP-hard even when all the rectangles are "anchored" at a line with slope -1.
Edit intent: clarity
Original:  It is easy to see that for the anchored rectangles , the problem reduces to one with even simpler objects: L-frames .
Revised:  It is easy to see that the MDS problem on "diagonal-anchored" rectangles is the same as the MDS problem on "diagonal-anchored" L-frames .
Edit intent: clarity
Original:  Glyph can be accessed at URL  Domain experts are be able to employ symbolic regression in their experiments with ease, even if they are not expert programmers.
Revised:  Glyph can be accessed at URL . Domain experts are be able to employ symbolic regression in their experiments with ease, even if they are not expert programmers.
Edit intent: fluency
Original: Message Passing Interface (MPI) is the standard paradigm of programming in high performance computing.
Revised: Message passing is the standard paradigm of programming in high performance computing.
Edit intent: clarity
Original:  This paper presents MPI symbolic verifier (MPI-SV), the first symbolic execution based tool for  verifying MPI programs having both blocking and non-blocking operations.
Revised:  This paper presents MPI symbolic verifier (MPI-SV), the first symbolic execution based tool for automatically verifying MPI programs having both blocking and non-blocking operations.
Edit intent: clarity
Original:  This paper presents MPI symbolic verifier (MPI-SV), the first symbolic execution based tool for  verifying MPI programs having both blocking and non-blocking operations.
Revised:  This paper presents MPI symbolic verifier (MPI-SV), the first symbolic execution based tool for verifying MPI programs with non-blocking operations.
Edit intent: clarity
Original:  We have implemented MPI-SV  and evaluated it on the verification of deadlock freedom for 108 real-world MPI  tasks.
Revised:  We have implemented MPI-SV and evaluated it on the verification of deadlock freedom for 108 real-world MPI verification tasks.
Edit intent: clarity
Original:  The pure symbolic execution based technique can successfully verify 61 out of the 108 tasks (56\%) within one hour, while in comparison, MPI-SV can verify 94 tasks (87\%), a 31\% improvement.
Revised:  The pure symbolic execution-based technique successfully verifies 61 out of the 108 tasks (56\%) within one hour, while in comparison, MPI-SV can verify 94 tasks (87\%), a 31\% improvement.
Edit intent: fluency
Original:  Our main contribution in this note is a new characterization of hyperbolicity for graphs(and for complete geodesic metric spaces) .
Revised:  The main contribution of this paper is a new characterization of hyperbolicity for graphs(and for complete geodesic metric spaces) .
Edit intent: clarity
Original:  Our main contribution in this note is a new characterization of hyperbolicity for graphs(and for complete geodesic metric spaces) .
Revised:  Our main contribution in this note is a new characterization of the hyperbolicity of graphs .
Edit intent: clarity
Original:  This characterization has algorithmic implications in the field of large-scale network analysis , which was one of our initial motivations .
Revised:  This characterization has algorithmic implications in the field of large-scale network analysis .
Edit intent: coherence
Original:  We demonstrate that  query nesting allows the definition of models which could not otherwise be expressed, such as those involving agents reasoning about other agents, but that existing systems take approaches that lead to inconsistent estimates.
Revised:  We demonstrate that while query nesting allows the definition of models which could not otherwise be expressed, such as those involving agents reasoning about other agents, but that existing systems take approaches that lead to inconsistent estimates.
Edit intent: coherence
Original:  We demonstrate that  query nesting allows the definition of models which could not otherwise be expressed, such as those involving agents reasoning about other agents, but that existing systems take approaches that lead to inconsistent estimates.
Revised:  We demonstrate that query nesting allows the definition of models which could not otherwise be expressed, such as those involving agents reasoning about other agents, existing systems take approaches that lead to inconsistent estimates.
Edit intent: coherence
Original:  We demonstrate that  query nesting allows the definition of models which could not otherwise be expressed, such as those involving agents reasoning about other agents, but that existing systems take approaches that lead to inconsistent estimates.
Revised:  We demonstrate that query nesting allows the definition of models which could not otherwise be expressed, such as those involving agents reasoning about other agents, but that existing systems take approaches which lead to inconsistent estimates.
Edit intent: fluency
Original:  We further introduce , and prove the correctness of, a new online nested Monte Carlo estimation method that makes it substantially easier to ensure these conditions are met, thereby providing a simple framework for designing statistically correct inference engines  .
Revised:  We further introduce a new online nested Monte Carlo estimation method that makes it substantially easier to ensure these conditions are met, thereby providing a simple framework for designing statistically correct inference engines .
Edit intent: coherence
Original:  We further introduce , and prove the correctness of, a new online nested Monte Carlo estimation method that makes it substantially easier to ensure these conditions are met, thereby providing a simple framework for designing statistically correct inference engines  .
Revised:  We further introduce , and prove the correctness of, a new online nested Monte Carlo estimator that makes it substantially easier to ensure these conditions are met, thereby providing a simple framework for designing statistically correct inference engines .
Edit intent: clarity
Original: Autonomous ridesharing systems (ARS) promise many societal and environmental benefits  including decreased accident rates, reduced energy consumption and pollutant emissions, and diminished land use for parking.
Revised: Autonomous ridesharing systems (ARS) promise many societal and environmental benefits , including decreased accident rates, reduced energy consumption and pollutant emissions, and diminished land use for parking.
Edit intent: fluency
Original: Based on an explicit equivalent continuous optimization problem, we propose a simple continuous iterative algorithm for Max Cut, which converges to a local optimum in finite steps .
Revised: We propose a simple continuous iterative algorithm for Max Cut, which converges to a local optimum in finite steps .
Edit intent: coherence
Original: Based on an explicit equivalent continuous optimization problem, we propose a simple continuous iterative algorithm for Max Cut, which converges to a local optimum in finite steps .
Revised: Based on an explicit equivalent continuous optimization problem, we propose a simple continuous iterative algorithm for Max Cut, which converges to a local optima in finite steps .
Edit intent: fluency
Original:  In particular, the ratio between the best cut values achieved by the simple algorithm without any local breakout techniques and the best known ones is of at least 0.986  .
Revised:  In particular, the ratios between the best cut values achieved by the simple algorithm without any local breakout techniques and the best known ones is of at least 0.986 .
Edit intent: fluency
Original:  In particular, the ratio between the best cut values achieved by the simple algorithm without any local breakout techniques and the best known ones is of at least 0.986  .
Revised:  In particular, the ratio between the best cut values achieved by the simple algorithm without any local breakout techniques and the best known ones are at least 0.986 .
Edit intent: clarity
Original: In the present work the computer modelling was used to show that longer ligands allow biological cells (e.g.  blood platelets) to withstand stronger flows after their adhesion to solid walls.
Revised: In this work the computer modelling was used to show that longer ligands allow biological cells (e.g. blood platelets) to withstand stronger flows after their adhesion to solid walls.
Edit intent: coherence
Original: In the present work the computer modelling was used to show that longer ligands allow biological cells (e.g.  blood platelets) to withstand stronger flows after their adhesion to solid walls.
Revised: In the present work the computer modeling has been used to show that longer ligands allow biological cells (e.g. blood platelets) to withstand stronger flows after their adhesion to solid walls.
Edit intent: clarity
Original: In the present work the computer modelling was used to show that longer ligands allow biological cells (e.g.  blood platelets) to withstand stronger flows after their adhesion to solid walls.
Revised: In the present work the computer modelling was used to show that longer ligands allow biological cells (e.g. , blood platelets) to withstand stronger flows after their adhesion to solid walls.
Edit intent: fluency
Original:  Mechanistic model of polymer-mediated ligand-receptor adhesion between a microparticle (cell) and a flat wall was developed.
Revised:  Mechanistic model of polymer-mediated ligand-receptor adhesion between a microparticle (cell) and a flat wall has been developed.
Edit intent: clarity
Original:  Theoretical threshold between adherent and non-adherent regimes was derived analytically and approved by the simulations.
Revised:  Theoretical threshold between adherent and non-adherent regimes has been derived analytically and approved by the simulations.
Edit intent: clarity
Original:  Theoretical threshold between adherent and non-adherent regimes was derived analytically and approved by the simulations.
Revised:  Theoretical threshold between adherent and non-adherent regimes was derived analytically and confirmed by simulations.
Edit intent: clarity
Original:  These results lead to  deeper understanding of numerous biophysical processes, e.g.  arterial thrombosis, and to the design of new biomimetic colloid-polymer systems.
Revised:  These results lead to a deeper understanding of numerous biophysical processes, e.g. arterial thrombosis, and to the design of new biomimetic colloid-polymer systems.
Edit intent: fluency
Original:  These results lead to  deeper understanding of numerous biophysical processes, e.g.  arterial thrombosis, and to the design of new biomimetic colloid-polymer systems.
Revised:  These results lead to deeper understanding of numerous biophysical processes, e.g. , arterial thrombosis, and to the design of new biomimetic colloid-polymer systems.
Edit intent: fluency
Original:  Building on ideas from the interactive theorem proving community we introduce Meta-F*, a metaprogramming framework for the F* effectful language and SMT-based program verification tool.
Revised:  Building on ideas from the interactive theorem proving community we introduce Meta-F*, a metaprogramming framework for F* effectful language and SMT-based program verification tool.
Edit intent: fluency
Original:  We evaluate Meta-F* on a variety of examples, demonstrating that tactics, and metaprogramming in general, improve proof stability and automation in F*.
Revised:  Beyond tactics, Meta-F* on a variety of examples, demonstrating that tactics, and metaprogramming in general, improve proof stability and automation in F*.
Edit intent: clarity
Original:  Meta-F* is not a new language: it is embedded into F* simply as a new, custom effect, which readily enables safe interactions between programs and metaprograms on equal footing.
Revised:  Meta-F* is implemented as an F* simply as a new, custom effect, which readily enables safe interactions between programs and metaprograms on equal footing.
Edit intent: clarity