wanyu/IteraTeR_v2 huggingface dataset:
Original:  Furthermore, we detail how a special case of our approach can be used for the robust denoising of periodic data, in particular for images  corrupted by wrapped Cauchy noise on the circle \mathbb S^1 .
Revised:  Furthermore, we detail how a special case of our approach can be used for the robust denoising of periodic data, in particular for images corrupted by wrapped Cauchy noise .
Edit intent: coherence
Original: This paper proposes a model for learning grid-like units for spatial awareness and navigation .
Revised: This paper proposes a representational model for grid cells .
Edit intent: clarity
Original:  In this model, the  self-position of the agent is represented by a  vector, and the  self-motion  of the agent is represented by a block-diagonal matrix . Each component of the vector is a unit ( or a cell ) .
Revised:  In this model, the self-position of the agent is represented by a vector, and the self-motion of the agent is represented by a block-diagonal matrix . Each component of the vector is a unit or a cell ) .
Edit intent: fluency
Original:  In this model, the  self-position of the agent is represented by a  vector, and the  self-motion  of the agent is represented by a block-diagonal matrix . Each component of the vector is a unit ( or a cell ) .
Revised:  In this model, the self-position of the agent is represented by a vector, and the self-motion of the agent is represented by a block-diagonal matrix . Each component of the vector is a unit ( or a cell .
Edit intent: fluency
Original:  The movement from the current position to the next position is modeled by matrix-vector multiplication, i.e.,  multiplying the matrix representation of the motion to the current vector representation of the position in order to obtain the vector representation of the next position . (2) Localization sub-model.
Revised:  The movement from the current position to the next position is modeled by matrix-vector multiplication, i.e., multiplying the matrix of the motion to the current vector representation of the position in order to obtain the vector representation of the next position . (2) Localization sub-model.
Edit intent: fluency
Original:  The movement from the current position to the next position is modeled by matrix-vector multiplication, i.e.,  multiplying the matrix representation of the motion to the current vector representation of the position in order to obtain the vector representation of the next position . (2) Localization sub-model.
Revised:  The movement from the current position to the next position is modeled by matrix-vector multiplication, i.e., multiplying the matrix representation of the motion to the vector of the current position . (2) Localization sub-model.
Edit intent: clarity
Original: Corporate mobility is often based on fixed assignments of vehicles to employees.
Revised: Corporate mobility is often based on a fixed assignment of vehicles to employees.
Edit intent: fluency
Original:  Relaxing these fixed assignments while including alternatives such as public transportation , bike sharing, and taxis for the employees' business and private trips could increase fleet utilization , foster the use of battery electric vehicles , and lower the costs for the companies' transportation needs.
Revised:  Relaxing this fixation while including alternatives such as public transportation , bike sharing, and taxis for the employees' business and private trips could increase fleet utilization , foster the use of battery electric vehicles , and lower the costs for the companies' transportation needs.
Edit intent: clarity
Original:  Relaxing these fixed assignments while including alternatives such as public transportation , bike sharing, and taxis for the employees' business and private trips could increase fleet utilization , foster the use of battery electric vehicles , and lower the costs for the companies' transportation needs.
Revised:  Relaxing these fixed assignments while including alternatives such as public transportation or taxis for business and private trips could increase fleet utilization , foster the use of battery electric vehicles , and lower the costs for the companies' transportation needs.
Edit intent: clarity
Original:  Relaxing these fixed assignments while including alternatives such as public transportation , bike sharing, and taxis for the employees' business and private trips could increase fleet utilization , foster the use of battery electric vehicles , and lower the costs for the companies' transportation needs.
Revised:  Relaxing these fixed assignments while including alternatives such as public transportation , bike sharing, and taxis for the employees' business and private trips could increase fleet utilization and foster the use of battery electric vehicles , and lower the costs for the companies' transportation needs.
Edit intent: coherence
Original:  In this work we introduce the NP-hard mobility offer allocation problem which has similarities to interval scheduling problems.
Revised:  In this work we introduce the NP-hard mobility offer allocation problem which is closely related to multi-interval scheduling problems.
Edit intent: clarity
Original:  In a computational study, the approaches are evaluated and it is demonstrated that, depending on instances and run-time requirements, either solving the model exactly using a general purpose integer linear programming solver , fast greedy heuristics, or the adaptive large neighborhood search outperforms the others.
Revised:  In a computational study, the approaches are evaluated and it is demonstrated that, depending on instances and run-time requirements, either a solver for the integer linear programming solver , fast greedy heuristics, or the adaptive large neighborhood search outperforms the others.
Edit intent: clarity
Original:  In a computational study, the approaches are evaluated and it is demonstrated that, depending on instances and run-time requirements, either solving the model exactly using a general purpose integer linear programming solver , fast greedy heuristics, or the adaptive large neighborhood search outperforms the others.
Revised:  In a computational study, the approaches are evaluated and it is demonstrated that, depending on instances and run-time requirements, either solving the model exactly using a general purpose integer linear programming model , fast greedy heuristics, or the adaptive large neighborhood search outperforms the others.
Edit intent: clarity
Original:  Relaxing this fixation while including alternatives such as public transportation or taxis for business and private trips could increase fleet utilization and foster the use of battery electric vehicles.
Revised:  Relaxing this fixation and including alternatives such as public transportation or taxis for business and private trips could increase fleet utilization and foster the use of battery electric vehicles.
Edit intent: coherence
Original:  Along this idea we propose a flexible booking system , leading to the introduction of the NP-hard mobilityoffer allocation problem which is closely related to multi-interval scheduling problems.
Revised:  We introduce the mobility offer allocation problem as the core concept of a flexible booking system , leading to the introduction of the NP-hard mobilityoffer allocation problem which is closely related to multi-interval scheduling problems.
Edit intent: clarity
Original:  In a computational study, the approaches are evaluated and it is demonstrated that , depending on instances and run-time requirements , either a solver for the integer linear programming model , fast greedy heuristics, or the adaptive large neighborhood search outperforms the others .
Revised:  In a computational study, the approaches are evaluated and it is demonstrated that , depending on instances and run-time requirements are given, a solver for the integer linear programming model , fast greedy heuristics, or the adaptive large neighborhood search outperforms the others .
Edit intent: clarity
Original:  In a computational study, the approaches are evaluated and it is demonstrated that , depending on instances and run-time requirements , either a solver for the integer linear programming model , fast greedy heuristics, or the adaptive large neighborhood search outperforms the others .
Revised:  In a computational study, the approaches are evaluated and it is demonstrated that , depending on instances and run-time requirements , either a solver for the integer linear programming model , fast greedy heuristics, or the adaptive large neighborhood search performs best on large instances .
Edit intent: clarity
Original: We briefly report on a  linear program reconstruction attack performed on a production statistical queries system and using a real dataset.
Revised: We briefly report on a successful linear program reconstruction attack performed on a production statistical queries system and using a real dataset.
Edit intent: clarity
Original: It has been developed a model of the DNA in MATLAB , where it has been taken into account each one of the component atoms.
Revised: This paper describes the model for DNA in MATLAB , where it has been taken into account each one of the component atoms.
Edit intent: clarity
Original: It has been developed a model of the DNA in MATLAB , where it has been taken into account each one of the component atoms.
Revised: It has been developed a model of the DNA in MATLAB taking into account all of component atoms.
Edit intent: clarity
Original:  It is possible to have a sequence length of even 10000 basis pairs with the possibility for introducing all types of sequences.
Revised:  In this model, it is possible to have a sequence length of even 10000 basis pairs with the possibility for introducing all types of sequences.
Edit intent: clarity
Original:  It is possible to have a sequence length of even 10000 basis pairs with the possibility for introducing all types of sequences.
Revised:  It is possible to generate sequences with length 10000 basis pairs with the possibility for introducing all types of sequences.
Edit intent: clarity
Original:  It is possible to have a sequence length of even 10000 basis pairs with the possibility for introducing all types of sequences.
Revised:  It is possible to have a sequence length of even 10000 basis pairs available for introducing all types of sequences.
Edit intent: clarity
Original:  It was studied the DNA damage in a single strain and in double strain, SSB and DSB respectively as a product of ionising radiation from X-rays when interacting with the DNA immersed in water.
Revised:  It was studied the DNA damage in the single strand and double strand. The damage are outcomes of ionising radiation from X-rays when interacting with the DNA immersed in water.
Edit intent: clarity
Original:  This is a theoretical and experimental study in-vitro  that quantifies the SSB and DSB with respect to different Gy's of radiation, this allows the understanding and prediction about the exact risks of the exposition.
Revised:  This is a theoretical and experimental study in-vitro that quantifies the single strand and double strand damage for different doses of radiation. This can be useful to predict the exact risks of the exposition.
Edit intent: clarity
Original:  The information of the spatial distribution of the electrones is obtained form Geant4 and afterwards it is implemented in Matlab where rays are created with tri-dimensional random trajectories through Monte Carlo simulations.
Revised:  The information of the spatial distribution of the electrons is obtained from Geant4 and afterwards it is implemented in Matlab where rays are created with tri-dimensional random trajectories through Monte Carlo simulations.
Edit intent: fluency
Original:  The information of the spatial distribution of the electrones is obtained form Geant4 and afterwards it is implemented in Matlab where rays are created with tri-dimensional random trajectories through Monte Carlo simulations.
Revised:  The information of the spatial distribution of the electrones is obtained form Geant4 and here this distribution is used for the creation of rays as three-dimensional random trajectories through Monte Carlo simulations.
Edit intent: clarity
Original:  It was obtained a direct relation between the damage and the radiation dose in the experiment and in the model and it is concluded that for 17.6 KeV the deterioration for interaction is observed very low doses but the mutagenic damage only appears until the 17 Gy .
Revised:  It was obtained a direct relation between the damage and the radiation doses with the experimental results .
Edit intent: clarity
Original:  Our extensive empirical results show that the Nesterov-accelerated ALS methods with restart can be dramatically more efficient than the stand-alone ALS or Nesterov accelerated gradient method , when problems are ill-conditioned or accurate solutions are required .
Revised:  Our extensive empirical results show that the Nesterov-accelerated ALS methods with restart can be dramatically more efficient than the stand-alone ALS or Nesterov accelerated gradient methods , when problems are ill-conditioned or accurate solutions are required .
Edit intent: fluency
Original:  Our extensive empirical results show that the Nesterov-accelerated ALS methods with restart can be dramatically more efficient than the stand-alone ALS or Nesterov accelerated gradient method , when problems are ill-conditioned or accurate solutions are required .
Revised:  Our extensive empirical results show that the Nesterov-accelerated ALS methods with restart can be dramatically more efficient than the stand-alone ALS or Nesterov accelerated gradient method , when problems are ill-conditioned or accurate solutions are desired .
Edit intent: clarity
Original:  The resulting methods perform competitively with or superior to existing acceleration methods for ALS,  and additionally enjoy the benefit of being much simpler and easier to implement.
Revised:  The resulting methods perform competitively with or superior to existing acceleration methods for ALS, and additionally enjoy the benefit of being much easier to implement.
Edit intent: clarity
Original:   On a large and ill-conditioned 71 x 1000 x 900 \times1000\times900 tensor consisting of readings from chemical sensors used for tracking hazardous gases, the restarted Nesterov-ALS method outperforms any of the existing methods by a large factor  .
Revised:  On a large and ill-conditioned 71 x 1000 x 900 \times1000\times900 tensor consisting of readings from chemical sensors to track hazardous gases, the restarted Nesterov-ALS method outperforms any of the existing methods by a large factor .
Edit intent: clarity
Original:  While Nesterov acceleration turns gradient descent into an optimal first-order method for convex problems by adding a momentum term with a specific weight sequence, a direct application of this method and weight sequence to ALS results in erratic convergence behaviour or divergence .
Revised:  While Nesterov acceleration turns gradient descent into an optimal first-order method for convex problems by adding a momentum term with a specific weight sequence, a direct application of this method and weight sequence to ALS results in erratic convergence behaviour .
Edit intent: clarity
Original:  This method relies on recent ideas coming from the particle filtering (PF) / sequential Monte-Carlo (SMC) literature.
Revised:  This method relies on recent ideas coming from the particle filtering / sequential Monte-Carlo (SMC) literature.
Edit intent: clarity
Original:  This method relies on recent ideas coming from the particle filtering (PF) / sequential Monte-Carlo (SMC) literature.
Revised:  This method relies on recent ideas coming from the particle filtering (PF) / sequential Monte-Carlo literature.
Edit intent: clarity
Original: We consider the algorithmic problem of computing the partition function of the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings .
Revised: We consider the algorithmic problem of exact computation of the partition function of the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings .
Edit intent: clarity
Original: We consider the algorithmic problem of computing the partition function of the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings .
Revised: We consider the algorithmic problem of computing the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings .
Edit intent: clarity
Original:  We show that there is no polynomial time algorithm for computing the partition function exactly (in the sense to be made precise), unless P = \#P.
Revised:  We show that there is no polynomial time algorithm to exactly compute the partition function exactly (in the sense to be made precise), unless P = \#P.
Edit intent: clarity
Original: We study the average-case hardness of the algorithmic problem of exact computation of the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings and random external field.
Revised: We establish the average-case hardness of the algorithmic problem of exact computation of the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings and random external field.
Edit intent: clarity
Original:  We establish that unless P=  P, there does not exist a polynomial time algorithm to exactly compute the partition function on average , by showing that if there exists a polynomial time algorithm, which exactly computes the partition function for inverse polynomial fraction (1/ nO(1) ) of all inputs, then there is a polynomial time algorithm, which exactly computes the partition function for all inputs, with high probability, yielding P=  P.
Revised:  In particular, we establish that unless P= P, there does not exist a polynomial time algorithm to exactly compute the partition function on average , by showing that if there exists a polynomial time algorithm, which exactly computes the partition function for inverse polynomial fraction (1/ nO(1) ) of all inputs, then there is a polynomial time algorithm, which exactly computes the partition function for all inputs, with high probability, yielding P= P.
Edit intent: coherence
Original:  We establish that unless P=  P, there does not exist a polynomial time algorithm to exactly compute the partition function on average , by showing that if there exists a polynomial time algorithm, which exactly computes the partition function for inverse polynomial fraction (1/ nO(1) ) of all inputs, then there is a polynomial time algorithm, which exactly computes the partition function for all inputs, with high probability, yielding P=  P.
Revised:  We establish that unless P= P, there does not exist a polynomial-time algorithm to exactly compute the partition function on average , by showing that if there exists a polynomial time algorithm, which exactly computes the partition function for inverse polynomial fraction (1/ nO(1) ) of all inputs, then there is a polynomial time algorithm, which exactly computes the partition function for all inputs, with high probability, yielding P= P.
Edit intent: fluency
Original:  We establish that unless P=  P, there does not exist a polynomial time algorithm to exactly compute the partition function on average , by showing that if there exists a polynomial time algorithm, which exactly computes the partition function for inverse polynomial fraction (1/ nO(1) ) of all inputs, then there is a polynomial time algorithm, which exactly computes the partition function for all inputs, with high probability, yielding P=  P.
Revised:  We establish that unless P= P, there does not exist a polynomial time algorithm to exactly compute the partition function on average . This is done by showing that if there exists a polynomial time algorithm, which exactly computes the partition function for inverse polynomial fraction (1/ nO(1) ) of all inputs, then there is a polynomial time algorithm, which exactly computes the partition function for all inputs, with high probability, yielding P= P.
Edit intent: clarity
Original:  and near-uniformity of the log-normal distribution, modulo a large prime p {\em   }\hspace{0pt} operating over real-valued inputs} .
Revised:  and near-uniformity of the log-normal distribution, modulo a large prime p {\em real-valued }\hspace{0pt} operating over real-valued inputs} .
Edit intent: fluency
Original:  We assume that rational (Bayesian) agents in this network make private measurements , and observe the decisions of their neighbors until they accumulate sufficient evidence to make an irreversible choice .
Revised:  We assume that rational (Bayesian) agents in this network make private measurements , and observe the decisions of their neighbors to make an irreversible choice .
Edit intent: clarity
Original:  Our model provides a bridge between the abstractions used in the economics literature and the evidence accumulator models used widely in neuroscience and psychology.
Revised:  Our model provides a bridge between social decision making models in the economics literature and the evidence accumulator models used widely in neuroscience and psychology.
Edit intent: clarity
Original:  Then based on this cost model, we develop an algorithm to calculate the optimal join tree for a given pattern.
Revised:  Then based on this cost model, we develop an algorithm to find the optimal join tree for a given pattern.
Edit intent: clarity
Original:  An extension to an Euler-Mahonian statistic over the set of ordered partitions presents itself naturally .
Revised:  Moreover, extensions to an Euler-Mahonian statistic over the set of ordered partitions presents itself naturally .
Edit intent: coherence
Original:  This leads to a large stochastic game, where each agents' performance criteria is computed under a different probability measure.
Revised:  This leads to a large stochastic game, where each agents' performance criteria are computed under a different probability measure.
Edit intent: fluency
Original:  We prove the MFG strategy forms an \epsilon-Nash equilibrium for the finite player game.
Revised:  Furthermore, we prove the MFG strategy forms an \epsilon-Nash equilibrium for the finite player game.
Edit intent: coherence
Original:  Methodology recently proposed by our group matches human accuracy by leveraging knowledge of the underlying physical process of these assays and using state-of-the-art iterative techniques to solve an inverse problem.
Revised:  Recently proposed methodology matches human accuracy by leveraging knowledge of the underlying physical process of these assays and using state-of-the-art iterative techniques to solve an inverse problem.
Edit intent: clarity
Original:  Methodology recently proposed by our group matches human accuracy by leveraging knowledge of the underlying physical process of these assays and using state-of-the-art iterative techniques to solve an inverse problem.
Revised:  Methodology recently proposed by our group matches human accuracy by leveraging knowledge of the underlying physical process of these assays and using proximal optimization methods to solve an inverse problem.
Edit intent: clarity
Original:  In this paper, we exploit the structure of the iterations to design a parameterized computation graph, SpotNet, that learns the characteristic patterns embedded within several training images and their respective cell secretion information.
Revised:  In this paper, we exploit the structure of the iterations to design a parameterized computation graph, SpotNet, that learns the patterns embedded within several training images and their respective cell secretion information.
Edit intent: clarity
Original:  In this paper, we exploit the structure of the iterations to design a parameterized computation graph, SpotNet, that learns the characteristic patterns embedded within several training images and their respective cell secretion information.
Revised:  In this paper, we exploit the structure of the iterations to design a parameterized computation graph, SpotNet, that learns the characteristic patterns embedded within several training images and their respective cell information.
Edit intent: clarity