wanyu/IteraTeR_v2 huggingface dataset:
Original:  Reducing  action potential onset rapidness can impair the ultrafast population encoding, but it is not clear whether rapid action potential onset is sufficient for ultrafast population encoding.
Revised:  Reducing action potential onset rapidness can impair the ultrafast population encoding, but it is not clear whether a sharp action potential onset is sufficient for ultrafast population encoding.
Edit intent: clarity
Original:  We find that  the axonal initiation site position is not sufficient to generate an ultrafast response and reproduce the high bandwidth observed in cortical neuron populations .
Revised:  We find that the ultrafast response and reproduce the high bandwidth observed in cortical neuron populations .
Edit intent: clarity
Original:  We find that  the axonal initiation site position is not sufficient to generate an ultrafast response and reproduce the high bandwidth observed in cortical neuron populations .
Revised:  We find that the axonal initiation site position is not sufficient to generate an ultrafast response and high bandwidth that is observed in cortical neuron populations .
Edit intent: clarity
Original:  We find that  the axonal initiation site position is not sufficient to generate an ultrafast response and reproduce the high bandwidth observed in cortical neuron populations .
Revised:  We find that the axonal initiation site position is not sufficient to generate an ultrafast response and reproduce the high bandwidth observed in cortical neurons .
Edit intent: clarity
Original:  By tuning the activation slope of the sodium current, we examined the impact of voltage sensitivity of sodium channels on population encoding.
Revised:  When we increase the voltage sensitivity of sodium channels on population encoding.
Edit intent: clarity
Original:  Our results show that high onset rapidness of action potential initiation is not sufficient for  ultrafast response.
Revised:  Our results show that a sharp onset of action potentials is not sufficient for ultrafast response.
Edit intent: clarity
Original:  Our results show that high onset rapidness of action potential initiation is not sufficient for  ultrafast response.
Revised:  Our results show that high onset rapidness of action potential initiation is not sufficient for the ultrafast response.
Edit intent: fluency
Original:  Using an adaptation of a construction by Bernardi and Chapuy, we can then derive a bijection between face-rooted toroidal d-angulations of essential girth d (with the condition that no d-angle encloses the root-face apart from its contour ) and a family of decorated unicellular maps.
Revised:  Using an adaptation of a construction by Bernardi and Chapuy, we can then derive a bijection between face-rooted toroidal d-angulations of essential girth d (with the condition that no d-angle encloses the root-face ) and a family of decorated unicellular maps.
Edit intent: clarity
Original:  The orientations and bijections can then be generalized  to toroidal face-rooted maps of essential girth d (for any d>= 1) with a root-face of degree d (and again no d-angle enclosing the root-face apart from its contour ), and they take a simpler form in the bipartite case, as a parity specialization.
Revised:  The orientations and bijections can then be generalized , for any d>=1, to toroidal face-rooted maps of essential girth d (for any d>= 1) with a root-face of degree d (and again no d-angle enclosing the root-face apart from its contour ), and they take a simpler form in the bipartite case, as a parity specialization.
Edit intent: fluency
Original:  The orientations and bijections can then be generalized  to toroidal face-rooted maps of essential girth d (for any d>= 1) with a root-face of degree d (and again no d-angle enclosing the root-face apart from its contour ), and they take a simpler form in the bipartite case, as a parity specialization.
Revised:  The orientations and bijections can then be generalized to toroidal face-rooted maps of essential girth d with a root-face of degree d (and again no d-angle enclosing the root-face apart from its contour ), and they take a simpler form in the bipartite case, as a parity specialization.
Edit intent: clarity
Original:  The orientations and bijections can then be generalized  to toroidal face-rooted maps of essential girth d (for any d>= 1) with a root-face of degree d (and again no d-angle enclosing the root-face apart from its contour ), and they take a simpler form in the bipartite case, as a parity specialization.
Revised:  The orientations and bijections can then be generalized to toroidal face-rooted maps of essential girth d (for any d>= 1) with a root-face of degree d (and with the same root-face apart from its contour ), and they take a simpler form in the bipartite case, as a parity specialization.
Edit intent: clarity
Original: Spatial networks are a very powerful framework for studying a large variety of systems which can be found in a broad diversity of contexts: from transportation , to biology, from epidemiology , to communications, and migrations, to cite a few.
Revised: Spatial networks are a very powerful framework for studying a large variety of systems which can be found in a broad diversity of contexts: from transportation to biology, from epidemiology , to communications, and migrations, to cite a few.
Edit intent: fluency
Original: Spatial networks are a very powerful framework for studying a large variety of systems which can be found in a broad diversity of contexts: from transportation , to biology, from epidemiology , to communications, and migrations, to cite a few.
Revised: Spatial networks are a very powerful framework for studying a large variety of systems which can be found in a broad diversity of contexts: from transportation , to biology, from epidemiology to communications, and migrations, to cite a few.
Edit intent: fluency
Original:  In spatial networks , distances between node pairs can be regarded as natural weights associated to links, generally understood as the  amount of resources needed for building or traveling such connections.
Revised:  In spatial networks , distances between node pairs can be regarded as natural weights associated to links, generally understood as the total amount of resources needed for building or traveling such connections.
Edit intent: clarity
Original:  Consequently, a network as a whole is characterized by atotal cost given by the sum of the costs of the links in them.
Revised:  Consequently, a network as a whole is characterized by a given by the sum of the costs of the links in them.
Edit intent: clarity
Original:  Consequently, a network as a whole is characterized by atotal cost given by the sum of the costs of the links in them.
Revised:  Consequently, a network as a whole is characterized by atotal cost their connections).
Edit intent: clarity
Original:  Hence, the smaller is the difference between the maximal and the empirical value of the quality function , the higher the quality of the design of the network .
Revised:  Hence, the smaller is the difference between such an upper bound and the empirical value of the quality function , the higher the quality of the design of the network .
Edit intent: clarity
Original:  Hence, the smaller is the difference between the maximal and the empirical value of the quality function , the higher the quality of the design of the network .
Revised:  Hence, the smaller is the difference between the maximal and the empirical value , the higher the quality of the design of the network .
Edit intent: clarity
Original:  Hence, the smaller is the difference between the maximal and the empirical value of the quality function , the higher the quality of the design of the network .
Revised:  Hence, the smaller is the difference between the maximal and the empirical value of the quality function , the higher we consider the design quality of the design of the network .
Edit intent: clarity
Original: Spatial networks are a very powerful framework for studying a large variety of systems which can be found in a broad diversity of contexts: from transportation to biology, from epidemiology to communications, and migrations, to cite a few.
Revised: Spatial networks are a powerful framework for studying a large variety of systems which can be found in a broad diversity of contexts: from transportation to biology, from epidemiology to communications, and migrations, to cite a few.
Edit intent: coherence
Original: Spatial networks are a very powerful framework for studying a large variety of systems which can be found in a broad diversity of contexts: from transportation to biology, from epidemiology to communications, and migrations, to cite a few.
Revised: Spatial networks are a very powerful framework for studying a large variety of systems belonging to a broad diversity of contexts: from transportation to biology, from epidemiology to communications, and migrations, to cite a few.
Edit intent: clarity
Original:  Spatial networks can be defined by their total cost ( generally understood as the total amount of resources needed for building or traveling their connections).
Revised:  Spatial networks can be described in terms of their total cost ( generally understood as the total amount of resources needed for building or traveling their connections).
Edit intent: clarity
Original:  Spatial networks can be defined by their total cost ( generally understood as the total amount of resources needed for building or traveling their connections).
Revised:  Spatial networks can be defined by their total cost ( i.e. the total amount of resources needed for building or traveling their connections).
Edit intent: clarity
Original:  Firstly, we introduce a quality function to assess the overall performance of any network .
Revised:  Firstly, we introduce a quality function based on the concept of network's efficiency .
Edit intent: clarity
Original:  Finally, we test the applicability of this analytic tool-set on spatial network datasets of different nature.
Revised:  Finally, we test the applicability of this analytic tool-set on spatial network data-sets of different nature.
Edit intent: fluency
Original:  In contrast, exactly counting compactions is the hardest of these problems.
Revised:  In contrast, exactly counting compactions is the hardest of all of these exact counting problems.
Edit intent: clarity
Original:  That is , they are traditionally finite probability spaces over database instances.
Revised:  Traditionally , they are traditionally finite probability spaces over database instances.
Edit intent: coherence
Original:  That is , they are traditionally finite probability spaces over database instances.
Revised:  That is , they are finite probability spaces over database instances.
Edit intent: clarity
Original:  Such  PDBs inherently make a closed-world assumption - non-occurring facts are assumed to be impossible, rather than just unlikely.
Revised:  Such PDBs inherently make a closed-world assumption : non-occurring facts are assumed to be impossible, rather than just unlikely.
Edit intent: fluency
Original:  As convincingly argued by Ceylan et al. (KR 2016 ), this results in implausibilities and clashes with intuition.
Revised:  As convincingly argued by Ceylan et al. (KR '16 ), this results in implausibilities and clashes with intuition.
Edit intent: fluency
Original:  The corresponding open-world model of Ceylan et al. however assumes that all entities in the PDB come from a fixed finite universe.
Revised:  The corresponding open-world model of Ceylan et al. , however, assumes that all entities in the PDB come from a fixed finite universe.
Edit intent: fluency
Original:  This is natural when we for example consider entities to be integers, real numbers  or strings.
Revised:  This is natural when we for example consider entities to be integers, real numbers , or strings.
Edit intent: fluency
Original:  We provide a sound mathematical framework for infinite PDBs in generalization of the existing theory on finite PDBs.
Revised:  We provide a sound mathematical framework for infinite PDBs generalizing the existing theory on finite PDBs.
Edit intent: fluency
Original:  We provide a sound mathematical framework for infinite PDBs in generalization of the existing theory on finite PDBs.
Revised:  We provide a sound mathematical framework for infinite PDBs in generalization of the existing theory of finite PDBs.
Edit intent: clarity
Original:  Our main results are concerned with  tuple-independent PDBs;
Revised:  Our main results are concerned with countable, tuple-independent PDBs;
Edit intent: clarity
Original:  This model can be used to apply open-world semantics to finite PDBs.
Revised:  This model can be used to give an open-world semantics to finite PDBs.
Edit intent: clarity
Original:  We  propose using the stochastic gradient descent (SGD) and its accelerated counterpart (ASGD) , which employs Nesterov's method, to solve the optimization problem in OED.
Revised:  We propose using the stochastic gradient descent and its accelerated counterpart (ASGD) , which employs Nesterov's method, to solve the optimization problem in OED.
Edit intent: coherence
Original:  We  propose using the stochastic gradient descent (SGD) and its accelerated counterpart (ASGD) , which employs Nesterov's method, to solve the optimization problem in OED.
Revised:  We propose using the stochastic gradient descent (SGD) and its accelerated counterpart , which employs Nesterov's method, to solve the optimization problem in OED.
Edit intent: clarity
Original:  From a theoretical viewpoint, we derive an explicit formula to compute the stochastic gradient of Monte Carlo with Laplace 's method.
Revised:  From a theoretical viewpoint, we derive an explicit formula to compute the stochastic gradient of Monte Carlo with Laplace method.
Edit intent: clarity
Original:  Finally, from a computational standpoint, we study four examples , being three based on analytical functions and one on the finite element method solution of a PDE.
Revised:  Finally, from a computational standpoint, we study four examples : three based on analytical functions and one on the finite element method solution of a PDE.
Edit intent: clarity
Original:  The latter is an electrical impedance tomography (EIT) experiment based on the complete electrode model  .
Revised:  The latter is an electrical impedance tomography experiment based on the complete electrode model .
Edit intent: clarity
Original: Finding the best set-up for the design of experiments is the main concern of Optimal Experimental Design (OED).
Revised: Finding the best setup for experiments is the main concern of Optimal Experimental Design (OED).
Edit intent: clarity
Original:  We focus on the Bayesian  problem of finding the set-up that maximizes the Shannon 's expected information gain.
Revised:  We focus on the Bayesian problem of finding the setup that maximizes the Shannon 's expected information gain.
Edit intent: fluency
Original:  We focus on the Bayesian  problem of finding the set-up that maximizes the Shannon 's expected information gain.
Revised:  We focus on the Bayesian problem of finding the set-up that maximizes the Shannon expected information gain.
Edit intent: clarity
Original:  We couple these optimization methods with three estimators of the objective function: a double loop Monte Carlo (DLMC), a Laplace approximation of the posterior distribution and a Laplace-based importance sampling .
Revised:  We couple these optimization methods with three estimators of the objective function: the double-loop Monte Carlo estimator (DLMC), a Laplace approximation of the posterior distribution and a Laplace-based importance sampling .
Edit intent: clarity
Original:  The use of stochastic gradient methods and Laplace-based estimators allow us to afford expensive and complex models, for example, those that require solving a partial differential equation (PDE).
Revised:  The use of stochastic gradient methods and Laplace-based estimators together allows us to use expensive and complex models, for example, those that require solving a partial differential equation (PDE).
Edit intent: clarity
Original:  The use of stochastic gradient methods and Laplace-based estimators allow us to afford expensive and complex models, for example, those that require solving a partial differential equation (PDE).
Revised:  The use of stochastic gradient methods and Laplace-based estimators allow us to afford expensive and complex models, such as those that require solving a partial differential equation (PDE).
Edit intent: coherence
Original:  Finally, from a computational standpoint, we study four examples: three based on analytical functions and one  on the finite element method solution of a PDE.
Revised:  Finally, from a computational standpoint, we study four examples: three based on analytical functions and one based on the finite element method solution of a PDE.
Edit intent: fluency
Original:  Finally, from a computational standpoint, we study four examples: three based on analytical functions and one  on the finite element method solution of a PDE.
Revised:  Finally, from a computational standpoint, we study four examples: three based on analytical functions and one on the finite element method solution to a PDE.
Edit intent: fluency
Original:  The latter is an electrical impedance tomography experiment based on the complete electrode model.
Revised:  The last example is an electrical impedance tomography experiment based on the complete electrode model.
Edit intent: clarity
Original:  The accelerated stochastic gradient with Laplace approximation converges to local maxima in fewer model evaluations by up to five orders of magnitude than  gradient descent with DLMC.
Revised:  The accelerated stochastic gradient with Laplace approximation converges to local maxima in fewer model evaluations by up to five orders of magnitude than the gradient descent with DLMC.
Edit intent: fluency
Original:  We propose using the stochastic gradient descent and its accelerated counterpart, which employs Nesterov's method, to solve the optimization problem in OED.
Revised:  We use the stochastic gradient descent and its accelerated counterpart, which employs Nesterov's method, to solve the optimization problem in OED.
Edit intent: coherence
Original:  We improve the stochastic gradient acceleration with a restart technique , as O'Donoghue and Candes originally proposed for deterministic optimization  .
Revised:  We adapt a restart technique , as O'Donoghue and Candes originally proposed for deterministic optimization .
Edit intent: clarity
Original:  From a theoretical viewpoint, we derive an explicit formula to compute the stochastic gradient of the Monte Carlo methods including the Laplace approximation (MCLA ) and the Laplace-based importance sampling (DLMCIS).
Revised:  From a theoretical viewpoint, we derive an explicit formula to compute the gradient estimator of the Monte Carlo methods including the Laplace approximation (MCLA ) and the Laplace-based importance sampling (DLMCIS).
Edit intent: clarity
Original:  Finally, from a computational standpoint, we study four examples: three based on analytical functions and one based on the finite element method solution to a PDE .
Revised:  Finally, from a computational standpoint, we study four examples: three based on analytical functions and one using on the finite element method solution to a PDE .
Edit intent: fluency
Original:  Finally, from a computational standpoint, we study four examples: three based on analytical functions and one based on the finite element method solution to a PDE .
Revised:  Finally, from a computational standpoint, we study four examples: three based on analytical functions and one based on the finite element method .
Edit intent: clarity
Original:  In these examples, the accelerated stochastic gradient for the MCLA approximation converges to local maxima in fewer model evaluations by up to five orders of magnitude than the gradient descent with DLMC.
Revised:  In these examples, the accelerated stochastic gradient descent method using MCLA converges to local maxima in fewer model evaluations by up to five orders of magnitude than the gradient descent with DLMC.
Edit intent: clarity
Original:  In these examples, the accelerated stochastic gradient for the MCLA approximation converges to local maxima in fewer model evaluations by up to five orders of magnitude than the gradient descent with DLMC.
Revised:  In these examples, the accelerated stochastic gradient for the MCLA approximation converges to local maxima in fewer model evaluations by up to five orders of magnitude than gradient descent with DLMC.
Edit intent: fluency
Original: Finding the best setup for experiments is the main concern of Optimal Experimental Design (OED).
Revised: Finding the best setup for experiments is the primary concern for Optimal Experimental Design (OED).
Edit intent: clarity
Original:  We focus on the Bayesian experimental design problem of finding the setup that maximizes the Shannon expected information gain.
Revised:  Here, we focus on the Bayesian experimental design problem of finding the setup that maximizes the Shannon expected information gain.
Edit intent: coherence
Original:  We adapt a restart technique to accelerated gradient-based algorithms , originally proposed for deterministic optimization problems , to improve the acceleration of the stochastic optimization .
Revised:  We adapt a restart technique , originally proposed for deterministic optimization problems , to improve the acceleration of the stochastic optimization .
Edit intent: clarity
Original:  We adapt a restart technique to accelerated gradient-based algorithms , originally proposed for deterministic optimization problems , to improve the acceleration of the stochastic optimization .
Revised:  We adapt a restart technique to accelerated gradient-based algorithms , originally proposed for the acceleration in deterministic optimization , to improve the acceleration of the stochastic optimization .
Edit intent: clarity
Original:  We adapt a restart technique to accelerated gradient-based algorithms , originally proposed for deterministic optimization problems , to improve the acceleration of the stochastic optimization .
Revised:  We adapt a restart technique to accelerated gradient-based algorithms , originally proposed for deterministic optimization problems , to improve stochastic optimization methods .
Edit intent: clarity
Original:  Using stochastic gradient methods and Laplace-based estimators together allows us to use expensive and complex models, such as those that require solving a partial differential equation (PDE ).
Revised:  Using stochastic gradient methods and Laplace-based estimators together allows us to use expensive and complex models, such as those that require solving partial differential equations (PDEs ).
Edit intent: fluency
Original:  From a theoretical viewpoint, we derive an explicit formula to compute the gradient estimator of the Monte Carlo methods  including MCLA and the DLMCIS.
Revised:  From a theoretical viewpoint, we derive an explicit formula to compute the gradient estimator of the Monte Carlo methods , including MCLA and the DLMCIS.
Edit intent: fluency
Original:  From a theoretical viewpoint, we derive an explicit formula to compute the gradient estimator of the Monte Carlo methods  including MCLA and the DLMCIS.
Revised:  From a theoretical viewpoint, we derive an explicit formula to compute the gradient estimator of the Monte Carlo methods including MCLA and DLMCIS.
Edit intent: fluency
Original:  From a computational standpoint, we study four examples: three based on analytical functions and one using on the finite element method.
Revised:  From a computational standpoint, we study four examples: three based on analytical functions and one using the finite element method.
Edit intent: fluency
Original:  In these examples, the accelerated stochastic gradient descent method using MCLA converges to local maxima in fewer model evaluations by up to five orders of magnitude  than gradient descent with DLMC.
Revised:  In these examples, the accelerated stochastic gradient descent method using MCLA converges to local maxima with up to five orders of magnitude than gradient descent with DLMC.
Edit intent: clarity